Hydrostatic Pressure

27 questions

All types27 Multiple choice13 Numeric7 Ordering7

An oceanarium features a massive main saltwater tank with several viewing windows and maintenance hatches of varying sizes. Arrange the following locations in order of the hydrostatic pressure exerted by the seawater at their center points, from the lowest pressure to the highest pressure.

Drag items to arrange them in the correct order

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Answer

The correct sequence from lowest to highest pressure corresponds strictly to depth: the 5-foot deep panoramic panel, the 10-foot deep porthole, the 15-foot deep observation window, and the 20-foot deep maintenance hatch.

Hydrostatic pressure is calculated based on the vertical depth below the surface. Because all windows are in the same saltwater tank, fluid density and gravity are constant. Therefore, the pressure increases linearly with depth, making the 5-foot depth the lowest pressure and the 20-foot depth the highest, regardless of the physical size of each window.

Step-by-Step Solution

Recall the principles determining hydrostatic pressure in a static fluid.

Hydrostatic pressure is determined by the equation

P = \rho gh

, meaning it depends only on fluid density (

\rho

), gravity (

g

), and depth (

h

Establishing the governing physical rule prevents confusion from irrelevant details like window size or shape.

Identify the relevant variable for each location.

The relevant variable is the depth of the center point for each window: 5 ft, 10 ft, 15 ft, and 20 ft.

Extracting the depth isolates the only factor that changes hydrostatic pressure in this single, uniform tank.

Sort the locations by depth to determine pressure order.

Ranking from lowest depth to highest depth gives: 5 ft < 10 ft < 15 ft < 20 ft.

Since pressure is directly proportional to depth, ordering from shallowest to deepest correctly ranks the pressure from lowest to highest.

Key Concept

Hydrostatic pressure in a static fluid is directly proportional to depth and is completely independent of the total fluid volume, container shape, or the area of the surface it acts upon.

Estimated Time:1m 0s

Question 22Question →

At a commercial fuel distribution center, two open-top vertical storage tanks hold the exact same grade of liquid diesel. Tank X is a wide cylinder with a $12\text{-meter}$ base diameter. Tank Y is a tall, narrow cylinder with a $2\text{-meter}$ base diameter. Both tanks are currently filled with diesel to an exact depth of $8\text{ meters}$ . Which of the following statements correctly compares the hydrostatic pressure exerted by the fuel on the bottom surface of each tank?

The pressure is identical in both tanks, because hydrostatic pressure depends only on fluid depth and density.

The pressure in Tank X is greater, because it contains a much larger total weight and volume of fuel.

The pressure in Tank Y is greater, because the narrower base restricts the fuel and concentrates its force.

The pressure cannot be compared without first calculating the total surface area of the tank walls.

Show answer & explanation

Answer: The pressure is identical in both tanks, because hydrostatic pressure depends only on fluid depth and density.

Answer

The pressure is identical in both tanks, because hydrostatic pressure depends only on fluid depth and density.

Hydrostatic pressure is determined by the formula

P = \rho gh

(where

\rho

is fluid density,

g

is gravity, and

h

is vertical fluid depth). Because both tanks hold the exact same fluid at the exact same depth, the pressure at the bottom is identical. The overall width, shape, or total volume of the tank does not affect hydrostatic pressure.

Step-by-Step Solution

Identify the standard formula for calculating hydrostatic pressure.

P = \rho \cdot g \cdot h

(Pressure = density

\times

gravity

\times

depth).

To determine which physical variables actually affect the pressure at the bottom of the fluid column.

Analyze the variables provided for both storage tanks.

Both tanks contain the exact same diesel fuel (identical density,

\rho

) and are filled to the same

8\text{-meter}

level (identical depth,

h

To compare the factors that influence hydrostatic pressure in this specific scenario.

Evaluate the effect of the different tank diameters (

12\text{ meters}

vs.

2\text{ meters}

The diameters and total fluid volumes do not appear in the hydrostatic pressure formula and therefore have no effect on the bottom pressure.

To confirm that the shape and width of the container are irrelevant to hydrostatic pressure at a given depth.

Key Concept

Hydrostatic pressure at a given depth depends strictly on the density of the fluid and the vertical depth itself, regardless of the container's shape, base width, or total fluid volume.

Question 23Question →

A hydrostatic pressure sensor at the bottom of an upright agricultural water cistern reads $45\text{ psi}$ when the water depth is $30\text{ feet}$ . During a dry season, the water level drops to a depth of $18\text{ feet}$ . Assuming the fluid density remains constant, what is the new hydrostatic pressure reading in $\text{psi}$ at the sensor?

Show answer & explanation

Answer: 27

Answer

Since hydrostatic pressure is directly proportional to depth (

P = \rho \cdot g \cdot h

), the ratio of pressure to depth remains constant. The initial ratio is

45\text{ psi} / 30\text{ feet} = 1.5\text{ psi/ft}

. At a new depth of

18\text{ feet}

, the pressure is

18\text{ feet} \times 1.5\text{ psi/ft} = 27\text{ psi}

Step-by-Step Solution

Identify the relationship between hydrostatic pressure and fluid depth.

Hydrostatic pressure is directly proportional to the depth of the fluid.

The formula for hydrostatic pressure is

P = \rho \cdot g \cdot h

, meaning if density (

\rho

) and gravity (

g

) are constant, the pressure changes linearly with depth (

h

Determine the pressure per foot of water depth.

45\text{ psi} \div 30\text{ feet} = 1.5\text{ psi}

per foot.

This establishes the constant of proportionality for the fluid in this specific cistern.

Calculate the new pressure at the reduced depth.

1.5\text{ psi/foot} \times 18\text{ feet} = 27\text{ psi}

Multiplying the pressure per foot by the new depth yields the corresponding hydrostatic pressure.

Key Concept

Hydrostatic pressure is directly proportional to fluid depth.

Question 24Question →

A structural engineer is evaluating two submerged sensor housings within a continuous freshwater facility. Housing X is mounted at the bottom of a narrow vertical standpipe, exactly $12\text{ meters}$ below the water's surface. Housing Y is mounted on the open floor of the main reservoir, also exactly $12\text{ meters}$ below the water's surface. Both locations share the same body of water. Which of the following statements correctly compares the hydrostatic pressure acting on the two housings?

The hydrostatic pressure is equal on both housings because they are situated at the identical vertical depth.

The hydrostatic pressure is greater on Housing Y because the expansive reservoir holds a much larger total weight of water.

The hydrostatic pressure is greater on Housing X because the narrow standpipe concentrates the fluid's downward force into a smaller area.

The hydrostatic pressure cannot be compared directly unless the depth measurements are mathematically converted into volumetric flow rates.

Show answer & explanation

Answer: The hydrostatic pressure is equal on both housings because they are situated at the identical vertical depth.

Answer

The hydrostatic pressure is equal on both housings because they are situated at the identical vertical depth.

The correct answer accurately states that hydrostatic pressure depends only on fluid depth. Because both housings are situated exactly

12\text{ meters}

below the surface of the same continuous body of water, the pressure exerted upon them is identical, regardless of the surrounding container geometry.

Step-by-Step Solution

Identify the factors that determine hydrostatic pressure.

Hydrostatic pressure (

P

) depends on fluid density (

\rho

), gravity (

g

), and vertical depth (

h

) according to the formula

P = \rho \cdot g \cdot h

This establishes the physical law governing the scenario.

Evaluate the fluid conditions for both housings.

Both housings are in the same continuous freshwater system, meaning the fluid density (

\rho

) is identical.

Eliminates fluid density as a variable between the two locations.

Compare the depth (

h

) and container shapes for both housings.

Housing X is in a narrow pipe at a

12\text{ m}

depth, and Housing Y is in a wide reservoir at a

12\text{ m}

depth. Container width and total fluid volume are not variables in the hydrostatic pressure formula.

Demonstrates that despite the drastically different container shapes, the equal depth guarantees equal pressure.

Key Concept

Hydrostatic pressure relies strictly on the vertical depth and density of the fluid, and is completely unaffected by the shape of the container or the total volume of the fluid.

Question 25Question →

A maintenance crew is inspecting a closed, static water pipeline fed by a mountain reservoir. They monitor static pressure sensors located at different points along the pipeline's path.

Arrange the following sensor locations in order from the LOWEST hydrostatic pressure to the HIGHEST hydrostatic pressure.

Drag items to arrange them in the correct order

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Answer

The correct order from lowest to highest pressure is: the surface sensor (0 feet), the sensor in the 24-inch pipe (30 feet), the sensor in the 12-inch pipe (60 feet), and the sensor at the bend (90 feet).

Hydrostatic pressure in a continuous, static fluid is directly proportional to its vertical depth below the free surface (

P = \rho g h

). Factors like pipe diameter, pipe orientation, or the total volume of fluid in a specific section do not influence the pressure at a specific point. Therefore, ranking from lowest to highest pressure simply requires ordering the depths from shallowest to deepest: 0 feet, 30 feet, 60 feet, and finally 90 feet.

Step-by-Step Solution

Identify the principle governing hydrostatic pressure in a static fluid.

Hydrostatic pressure is determined by the formula

P = \rho g h

, where

h

is the vertical depth from the free surface of the fluid.

Establishing the core rule is necessary to evaluate which variables provided in the scenario actually affect the pressure.

Evaluate the effect of pipe diameter and shape on the pressure.

The 12-inch diameter, 24-inch diameter, and horizontal pipe bend do not affect static pressure.

According to Pascal's principle and fluid statics, pressure at a given depth is independent of the container's volume, shape, or width.

Rank the locations based solely on their vertical depth below the reservoir surface.

Surface (0 ft) < 30 ft < 60 ft < 90 ft.

Since vertical depth is the only changing variable that affects the pressure, the ranking strictly follows the depth from shallowest to deepest.

Key Concept

Hydrostatic pressure in a continuous fluid depends exclusively on fluid density, gravity, and vertical depth, remaining entirely independent of the container's volume or shape.

Question 26Question →

A hydroelectric dam holds back a massive artificial lake. Along the submerged face of the dam, there is a small diagnostic sensor port and a massive turbine water intake. Both the sensor port and the center of the turbine intake are located exactly $45\text{ meters}$ below the surface of the lake. The diameter of the turbine intake is twenty times larger than the diagnostic port. When the water in the lake is perfectly still, how does the hydrostatic pressure at the diagnostic port compare to the pressure at the center of the turbine intake?

The pressure is identical at both locations because they are positioned at the exact same depth.

The pressure is twenty times greater at the turbine intake because its larger diameter captures more force from the water.

The pressure is significantly higher at the diagnostic port because the fluid is compressed into a narrower opening.

The pressure at both locations is determined by the total mass of the reservoir, so the depth of the specific openings is not the primary factor.

Show answer & explanation

Answer: The pressure is identical at both locations because they are positioned at the exact same depth.

Answer

The pressure is identical at both locations because they are positioned at the exact same depth.

Hydrostatic pressure in a static fluid is calculated using the formula

P = \rho g h

(Pressure = density × gravity × depth). Because both the diagnostic port and the center of the turbine intake are located exactly

45\text{ meters}

below the surface, they experience the exact same water pressure. The size, diameter, or area of the opening affects the total force exerted on that opening, but it does not change the pressure, which is a measure of force per unit area.

Step-by-Step Solution

Identify the factors that determine hydrostatic pressure in a static fluid.

Hydrostatic pressure (

P

) is determined by the formula

P = \rho g h

, where

\rho

is fluid density,

g

is gravity, and

h

is depth.

This establishes the physical rule governing the scenario, showing that only depth matters when the fluid is consistent.

Compare the depth of the two locations provided in the scenario.

Both the diagnostic port and the turbine intake center are located at a depth of

45\text{ meters}

Since the

h

value is identical for both locations, the pressure calculated from

P = \rho g h

will be equal.

Evaluate the effect of the opening sizes on the hydrostatic pressure.

The diameter of the openings has no effect on the hydrostatic pressure, though it does affect the total force (

F = P \times A

It separates the concept of pressure (force per unit area) from the concept of total force, confirming that the pressure remains identical.

Key Concept

Hydrostatic pressure in a liquid depends only on the depth of the liquid and its density, and is entirely independent of the shape or size of the container or opening.

Question 27Question →

A vertical ballast column on a maritime vessel is completely filled with fresh water. A pressure gauge is mounted precisely $60\text{ feet}$ below the open surface of the water. If the specific weight of the fresh water is $62.4\text{ lb/ft}^3$ , what is the hydrostatic gauge pressure at this depth in pounds per square inch (psi)?

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Answer: 26

Answer

The hydrostatic pressure is 26 psi.

The correct calculation requires two phases: first, determining the pressure based on depth and specific weight, which yields

3744\text{ psf}

(

60 \times 62.4

). Second, converting area units from square feet to square inches by dividing by 144, resulting in exactly

26\text{ psi}

Step-by-Step Solution

Calculate the hydrostatic pressure in pounds per square foot (psf).

62.4\text{ lb/ft}^3 \times 60\text{ ft} = 3744\text{ lb/ft}^2

(psf)

Hydrostatic pressure is the product of the fluid's specific weight and the depth of the fluid column.

Convert the pressure from psf to pounds per square inch (psi).

3744\text{ psf} \div 144\text{ in}^2/\text{ft}^2 = 26\text{ psi}

There are

144\text{ square inches}

1\text{ square foot}

(

12\text{ inches} \times 12\text{ inches}

). Dividing the psf value by 144 converts the units appropriately.

Key Concept

Hydrostatic Pressure Calculation and Unit Conversion

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