Fluid Dynamics and Bernoulli's Principle

11 questions

All types11 Multiple choice5 True / False4 Ordering2

When a steady flow of fluid passes through a horizontal pipe that suddenly narrows in diameter, the fluid's velocity increases in the constricted section, resulting in a higher static pressure against the pipe walls.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because Bernoulli's principle dictates that as a fluid's velocity increases in a constricted horizontal pipe, its static pressure decreases, creating a low-pressure zone rather than a high-pressure one.

Step-by-Step Solution

Analyze the change in fluid velocity through the constriction.

Based on the continuity equation (

A_1V_1 = A_2V_2

), the fluid's velocity increases as it enters the narrower section of the pipe.

The same volume of fluid must pass through a smaller area in the same amount of time, requiring it to speed up.

Determine the effect of increased velocity on static pressure.

Static pressure decreases.

Bernoulli's principle states that for a horizontal flow, an increase in the speed of the fluid occurs simultaneously with a decrease in static pressure.

Evaluate the statement's claim against the established physical principles.

The statement claims static pressure increases, which contradicts the actual outcome (a decrease in static pressure).

The inverse relationship between fluid velocity and static pressure confirms the statement is false.

Key Concept

Bernoulli's principle and the continuity equation for incompressible fluids.

Estimated Time:45s

Question 2Question →

Evaluate whether the following statement is true or false:

In a mechanical carburetor, outside air flows through a narrow central constriction. As the air accelerates and its velocity increases through this narrow section, the static pressure of the air increases, forcing fuel to mix into the airstream.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because Bernoulli's principle establishes an inverse relationship between a fluid's velocity and its static pressure. As the air accelerates through the carburetor's narrow constriction, its static pressure drops, creating a low-pressure area (a partial vacuum) that siphons fuel into the airstream, rather than an area of increased pressure.

Step-by-Step Solution

Recall Bernoulli's principle regarding fluid velocity and static pressure.

Bernoulli's principle states that as the velocity of a fluid increases, its static pressure decreases.

Establishing the fundamental physical law governing fluids moving through a constriction.

Evaluate the claim made in the statement.

The statement incorrectly claims that an increase in air velocity causes the static pressure to increase.

Comparing the scenario's claim directly against the established physics principle to determine its validity.

Key Concept

Inverse relationship between fluid velocity and static pressure (Bernoulli's Principle)

Question 3Question →

During flight, an aircraft wing (airfoil) is designed so that air travels significantly faster over its curved upper surface compared to its flatter lower surface. According to Bernoulli's principle, what is the result of this difference in air velocity?

The static pressure above the wing becomes lower than the pressure below it, generating upward lift.

The faster-moving air above the wing generates higher static pressure, which pulls the aircraft upward.

The difference in air speed creates a buoyant force based on the displaced weight of the air, lifting the wing.

The faster air over the top of the wing compresses tightly, increasing its density and pushing the wing upward.

Show answer & explanation

Answer: The static pressure above the wing becomes lower than the pressure below it, generating upward lift.

Answer

The static pressure above the wing becomes lower than the pressure below it, generating upward lift.

According to Bernoulli's principle, as the velocity of a fluid (such as air) increases, its static pressure decreases. Because the wing is shaped to make the air travel faster over its top surface, a region of low pressure is created above the wing. The slower-moving air beneath the wing maintains a relatively higher pressure. This difference in pressure—high on the bottom, low on the top—results in a net upward force that lifts the aircraft.

Step-by-Step Solution

Recall the fundamental rule of Bernoulli's principle regarding fluid flow.

In a flowing fluid, an increase in velocity is accompanied by a decrease in static pressure.

This inverse relationship is the core concept of Bernoulli's principle.

Apply the principle to the specific scenario of the aircraft wing described in the question.

The air moving over the top of the wing has a higher velocity than the air moving underneath. Therefore, the static pressure on the top surface must be lower than the static pressure on the bottom surface.

Mapping the physical conditions (faster top, slower bottom) to the principle reveals the pressure distribution.

Determine the physical consequence of this pressure difference.

The relatively higher pressure beneath the wing pushes upward toward the area of lower pressure above the wing, creating a net upward force known as lift.

Objects are naturally pushed from areas of higher pressure toward areas of lower pressure.

Key Concept

According to Bernoulli's principle, an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. This pressure differential across surfaces like airfoils creates mechanical forces such as lift.

Estimated Time:45s

Question 4Question →

Water flows at a steady rate through a horizontal pipe that consists of four distinct sections with different diameters. According to Bernoulli's principle and the continuity equation, arrange the pipe sections in order of their static pressure, from the lowest static pressure to the highest static pressure.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from lowest to highest static pressure is: Section W (1-inch), Section X (2-inch), Section Y (3-inch), Section Z (4-inch).

According to the continuity equation, a fluid travels faster through a narrower section of pipe. According to Bernoulli's principle, an increase in fluid velocity results in a decrease in static pressure. Therefore, the pipe sections with the smallest diameters will have the highest velocities and the lowest static pressures, while the sections with the largest diameters will have the lowest velocities and the highest static pressures.

Step-by-Step Solution

Determine the relationship between the pipe's diameter and the fluid's velocity.

The continuity equation indicates that fluid must travel faster through narrower sections to maintain a steady flow rate. Therefore, the smallest diameter has the highest velocity, and the largest diameter has the lowest velocity.

Because the volume of fluid passing through any section per second must remain constant.

Determine the relationship between fluid velocity and static pressure.

Bernoulli's principle states that an increase in fluid velocity occurs simultaneously with a decrease in static pressure.

The total energy in a steady, horizontal fluid flow is constant; as kinetic energy (speed) increases, pressure potential energy must decrease.

Rank the sections based on these relationships.

Since smallest diameter = highest velocity = lowest pressure, the order from lowest to highest pressure corresponds exactly to the order from smallest to largest diameter.

This allows us to arrange the sections directly by their diameter sizes: 1-inch, 2-inch, 3-inch, and 4-inch.

Key Concept

Fluid Dynamics and Bernoulli's Principle

Question 5Question →

A common paint sprayer operates by blowing a stream of fast-moving air across the top of an open vertical tube, with the bottom of the tube submerged in a container of paint. Based on Bernoulli's principle, what is the primary reason the paint rises up the tube?

The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

The high-speed air creates a region of high static pressure at the top of the tube, which pulls the paint upward.

The stream of air compresses the fluid inside the vertical tube, reducing its volume and forcing it upward.

The fast-moving air decreases the weight of the displaced fluid, causing an upward buoyant force.

Show answer & explanation

Answer: The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

Answer

The fast-moving air creates a region of low static pressure at the top of the tube, allowing atmospheric pressure to push the paint upward.

According to Bernoulli's principle, an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. The fast-moving air across the top of the tube creates a localized low-pressure area. The relatively higher atmospheric pressure pushing down on the surface of the paint in the container then forces the liquid up the tube.

Step-by-Step Solution

Analyze the relationship between fluid speed and pressure.

The air moving quickly across the top of the tube has a higher velocity than the still air surrounding the container.

This scenario directly sets up an application of Bernoulli's principle.

Determine the pressure difference.

Due to its high velocity, the air stream creates an area of low static pressure directly above the open tube.

Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in its static pressure.

Evaluate the effect on the fluid in the container.

The standard atmospheric pressure resting on the surface of the paint in the container is greater than the low pressure at the top of the tube, thus forcing the paint upward into the stream.

Fluids naturally move from areas of higher pressure to areas of lower pressure.

Key Concept

Bernoulli's principle establishes an inverse relationship between a fluid's velocity and its static pressure.

Estimated Time:45s

Question 6Question →

Two ships are traveling parallel to each other at high speed, leaving a narrow channel of water between their hulls. The water flowing into this narrow space moves at a significantly higher relative velocity than the water on the outer sides of the ships. According to Bernoulli's principle, what happens to the water pressure in the gap, and what is the resulting effect on the two ships?

The water pressure in the gap decreases, creating a net inward force that pulls the ships toward each other.

The water pressure in the gap increases due to the higher velocity, creating a net outward force that pushes the ships apart.

The water compresses as it enters the narrow gap, causing the pressure to increase and violently push the ships apart.

The water pressure remains unchanged, but the increased fluid friction in the gap creates a drag force that pushes the ships apart.

Show answer & explanation

Answer: The water pressure in the gap decreases, creating a net inward force that pulls the ships toward each other.

Answer

The water pressure in the gap decreases, creating a net inward force that pulls the ships toward each other.

According to Bernoulli's principle, an increase in fluid velocity is accompanied by a decrease in static pressure. Because the water between the parallel ships is forced to flow faster through the narrow gap, the pressure in that specific region drops. The relatively slower-moving water on the outer sides of the ships maintains a higher pressure. This pressure differential creates a net inward force, pushing the two vessels toward each other.

Step-by-Step Solution

Identify the relationship between fluid velocity and static pressure.

Bernoulli's principle states that as the speed of a moving fluid increases, its static pressure decreases.

This is the fundamental concept governing fluid dynamics in constricted flow areas.

Apply the principle to the given maritime scenario.

The water channeled between the ships moves faster relative to the hulls than the water on the outside. Therefore, the static pressure between the hulls becomes lower than the static pressure on the outer sides of the ships.

The narrowing of the channel forces the water to speed up to maintain continuous flow, which directly affects the localized pressure.

Determine the resulting physical force acting on the vessels.

The higher pressure on the outside of the ships pushes inward toward the lower pressure zone between them, effectively drawing the ships together.

Fluids exert a net force moving from high-pressure areas toward low-pressure areas.

Key Concept

Bernoulli's Principle and Pressure Differentials

Question 7Question →

When a steady flow of water moves from a wide horizontal pipe into a narrower section, the water's velocity increases, causing the static pressure against the walls of the narrow section to be higher than in the wider section.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false because Bernoulli's principle dictates that as the velocity of a horizontal fluid flow increases (which it must do when entering a narrower pipe to maintain flow rate), its static pressure decreases. Therefore, the pressure against the walls is lower, not higher, in the narrow section.

Step-by-Step Solution

Determine the change in fluid velocity.

The water's velocity increases as it enters the narrow section.

The principle of continuity states that for an incompressible fluid, the flow rate must remain constant; thus, a smaller cross-sectional area requires a higher velocity.

Relate the change in velocity to static pressure.

The static pressure in the narrow section decreases.

Bernoulli's principle states that in a steady, horizontal fluid flow, an increase in fluid velocity results in a decrease in static pressure because total energy is conserved.

Evaluate the original statement.

The statement is false.

The statement incorrectly claims that the static pressure would be higher in the narrow section, when in fact it is lower.

Key Concept

Bernoulli's Principle and Fluid Continuity

Question 8Question →

A mechanical eductor (or jet pump) uses a primary fluid flowing through a converging nozzle to extract a secondary fluid from a lower tank. As the primary fluid accelerates through the narrowest section of the nozzle, how does its static pressure change, and what is the resulting effect on the secondary fluid?

The static pressure rises proportionally with the fluid's velocity, creating a force that pushes the secondary fluid forward.

The increased friction against the narrow nozzle walls creates a high-pressure zone that drives the secondary fluid upward.

The static pressure drops below the surrounding pressure, creating a suction effect that draws the secondary fluid into the main stream.

The static pressure remains constant because liquids are incompressible, and the fluids mix solely due to physical contact.

Show answer & explanation

Answer: The static pressure drops below the surrounding pressure, creating a suction effect that draws the secondary fluid into the main stream.

Answer

The static pressure drops below the surrounding pressure, creating a suction effect that draws the secondary fluid into the main stream.

The correct answer accurately applies Bernoulli's principle, which states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure. In an eductor, the narrow nozzle accelerates the primary fluid, causing a significant pressure drop. This localized low-pressure zone acts as a vacuum, drawing the secondary fluid from the tank into the main flow.

Step-by-Step Solution

Analyze the fluid flow through the converging nozzle.

The cross-sectional area of the nozzle decreases, which forces the fluid velocity to increase in order to maintain a constant flow rate (continuity principle).

Understanding how area affects velocity is the first step in applying fluid dynamics.

Apply Bernoulli's principle to the high-velocity region.

According to Bernoulli's equation, an increase in fluid velocity (kinetic energy) must be accompanied by a decrease in static pressure to conserve total mechanical energy.

This establishes the inverse relationship between velocity and static pressure.

Determine the physical consequence of the lowered static pressure.

The decreased static pressure in the narrow section becomes lower than the atmospheric pressure acting on the secondary fluid, creating a pressure differential (suction) that draws the secondary fluid up into the eductor.

This links the theoretical physics concept directly to the mechanical action described in the problem.

Key Concept

As a fluid's velocity increases, its static pressure decreases, which can be utilized to create suction in mechanical systems.

Estimated Time:1m 0s

Question 9Question →

A steady stream of water flows through a horizontal pipeline of varying diameter. Four vertical piezometer tubes (standpipes open to the atmosphere) are installed along the pipe to measure the local static pressure. The height of the water column in each tube is observed as follows:

- Station 1: $1.2$ meters
- Station 2: $2.5$ meters
- Station 3: $0.8$ meters
- Station 4: $1.8$ meters

Based on Bernoulli's principle, arrange the stations in order from the fastest fluid velocity to the slowest fluid velocity.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from fastest to slowest velocity is: Station 3, Station 1, Station 4, Station 2.

According to Bernoulli's principle, for an incompressible fluid flowing through a horizontal pipe, an increase in fluid velocity occurs simultaneously with a decrease in static pressure. The height of the water in a vertical piezometer tube is a direct measure of the static pressure at that location. Therefore, the station with the lowest water column (Station 3,

0.8

m) has the lowest static pressure and the fastest velocity. The station with the highest water column (Station 2,

2.5

m) has the highest static pressure and the slowest velocity. Sorting from lowest to highest water column gives the correct sequence from fastest to slowest velocity.

Step-by-Step Solution

Understand the relationship between water column height and static pressure.

The height of a fluid column in a piezometer tube directly indicates the static pressure at that point (

P = \rho g h

Establishing what the given measurements represent.

Apply Bernoulli's principle to relate static pressure and fluid velocity.

In a horizontal pipe, regions with higher static pressure correspond to slower fluid velocities, and regions with lower static pressure correspond to faster fluid velocities.

This inverse relationship is the core concept of Bernoulli's principle for steady, horizontal flow.

Rank the static pressures based on the water column heights.

Lowest pressure to highest pressure: Station 3 (

0.8

m), Station 1 (

1.2

m), Station 4 (

1.8

m), Station 2 (

2.5

m).

To find the order of fluid velocities, we first need to order the static pressures.

Determine the final order of fluid velocities.

Since the fastest velocity occurs at the lowest pressure, the order from fastest to slowest is: Station 3, Station 1, Station 4, Station 2.

Translating the pressure ranking into the final velocity ranking required by the question.

Key Concept

Fluid Dynamics and Bernoulli's Principle

Estimated Time:1m 30s

Question 10Question →

During routine maintenance of a municipal water line, engineers observe that a thick layer of mineral scale has formed inside a section of a horizontal supply pipe. This scale acts as a partial blockage, significantly reducing the pipe's interior cross-sectional area in that specific location. Assuming the flow rate of water through the system remains steady, how are the water's velocity and static pressure affected as it passes through this narrowed section?

The water's velocity increases, and its static pressure also increases due to the confined space.

The water's velocity decreases due to the restricted opening, causing the static pressure to drop.

The water's velocity increases, and its static pressure decreases.

The water's velocity remains constant, but its static pressure increases because the liquid is compressed.

Show answer & explanation

Answer: The water's velocity increases, and its static pressure decreases.

Answer

The water's velocity increases, and its static pressure decreases.

In a closed, continuous fluid system, an incompressible liquid like water must maintain a constant flow rate. When it encounters a constriction (like the mineral scale buildup), the only way the same volume of water can get through the smaller opening in the same amount of time is to speed up (principle of continuity). As the velocity increases, Bernoulli's principle dictates that the static pressure must decrease so that the total energy of the fluid flow remains constant.

Step-by-Step Solution

Determine the change in velocity through the narrowed pipe section.

The velocity of the water increases.

Because water is an incompressible fluid, the same volume of water must pass through the restricted area in the same amount of time. This relies on the principle of continuity (

A_1V_1 = A_2V_2

). To maintain the flow rate through a smaller cross-sectional area (

A

), the velocity (

V

) must increase.

Determine the change in static pressure based on the new velocity.

The static pressure of the water decreases.

According to Bernoulli's principle, the total mechanical energy in a steady horizontal fluid flow remains constant. When the water's kinetic energy increases (due to higher velocity), its potential energy—manifested as static pressure against the pipe walls—must decrease proportionally to conserve energy.

Key Concept

Fluid Dynamics and Bernoulli's Principle

Estimated Time:45s

Question 11Question →

As a race car travels at high speeds, the air flowing through the narrow clearance between the car's flat underbody and the track surface accelerates. According to the principles of fluid dynamics, this increase in air velocity creates a region of elevated static pressure that pushes upward against the bottom of the car.

True

False

Show answer & explanation

Answer: False

Answer

False

The statement is false. According to Bernoulli's principle, an increase in fluid velocity results in a decrease in static pressure. Therefore, the fast-moving air under the race car creates a low-pressure zone that produces downforce, rather than an upward push.

Step-by-Step Solution

Analyze the change in air velocity under the vehicle.

The narrow gap between the car's underbody and the track restricts the airflow area, causing the air velocity to increase in order to maintain a continuous flow.

The continuity equation dictates that fluid velocity must increase when the cross-sectional area of the flow path decreases.

Relate the increased velocity to static pressure using Bernoulli's principle.

According to Bernoulli's principle, the higher kinetic energy of the fast-moving air results in a simultaneous decrease in static pressure.

In a flowing fluid system, an increase in velocity is accompanied by a drop in static pressure to conserve total energy.

Determine the direction of the resulting force on the vehicle.

Because the static pressure under the car decreases, the relatively higher ambient pressure above the car pushes it downward, creating downforce rather than upward lift.

Objects are naturally pushed toward regions of lower pressure.

Key Concept

Bernoulli's Principle and the Continuity Equation

Fluid Dynamics and Bernoulli's Principle

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