Arrange the following points in a fluid system in order of their gauge hydrostatic pressur… — Armed Services Vocational Aptitude Battery (ASVAB)

Arrange the following points in a fluid system in order of their gauge hydrostatic pressure, from the GREATEST pressure to the LEAST pressure. Assume standard gravity applies equally to all systems.

1A point at the bottom of a $15$ -meter tall, narrow vertical pipe completely filled with oil (Specific Gravity = $0.8$ ).
2A point at the bottom of a massive, wide cylindrical vat containing $5$ meters of water (Specific Gravity = $1.0$ ) floating on top of $5$ meters of glycerin (Specific Gravity = $1.3$ ).
3A point $11$ meters deep in a natural freshwater lake (Specific Gravity = $1.0$ ).
4A point $9$ meters deep in a standard rectangular tank of dense brine (Specific Gravity = $1.2$ ).
5A point at the bottom of an inverted conical vessel filled with $14$ meters of gasoline (Specific Gravity = $0.7$ ).

Cevap

The correct order from greatest to least pressure is: the

15

-meter oil pipe, the layered vat, the

11

-meter lake, the

9

-meter brine tank, and finally the

14

-meter conical vessel.

By calculating the equivalent water depth (Depth

\times

Specific Gravity) for each scenario, we find the values are

12.0

(pipe),

11.5

(layered vat),

11.0

(lake),

10.8

(brine tank), and

9.8

(conical vessel). Ranking these from highest to lowest provides the correct sequence.

Adım Adım Çözüm

Recall the formula for hydrostatic pressure.

P = \rho \cdot g \cdot h

, where

\rho

is density,

g

is gravity, and

h

is depth.

This establishes that pressure depends solely on fluid density and depth, not on container shape or total volume.

Determine a standard unit for comparison across all items.

Use 'equivalent meters of water' by multiplying the depth of each fluid by its Specific Gravity (SG).

This simplifies calculations and provides a single proportional metric to compare.

Calculate the equivalent pressure for the single-fluid containers.

Pipe:

15 \times 0.8 = 12.0

. Lake:

11 \times 1.0 = 11.0

. Brine:

9 \times 1.2 = 10.8

. Conical vessel:

14 \times 0.7 = 9.8

Applying the formula directly to the given depth and Specific Gravity.

Calculate the equivalent pressure for the layered fluids in the vat.

Top layer (water):

5 \times 1.0 = 5.0

. Bottom layer (glycerin):

5 \times 1.3 = 6.5

. Total equivalent depth =

5.0 + 6.5 = 11.5

The total pressure at the bottom of layered fluids is the sum of the hydrostatic pressures of each individual layer.

Rank the calculated equivalent water depths from greatest to least.

12.0 > 11.5 > 11.0 > 10.8 > 9.8

This corresponds to the final required ordering.

Anahtar Kavram

Hydrostatic pressure is determined solely by fluid density and depth, completely independent of the container's shape, width, or total fluid volume.

Alternatif Yöntem

Instead of calculating equivalent water depth, you can calculate exact pressure if you assign

g = 9.8 \text{ m/s}^2

and density of water as

1000 \text{ kg/m}^3

. For example, the pipe pressure is

0.8 \times 1000 \times 9.8 \times 15 = 117,600 \text{ Pa}

. However, comparing the relative

(h \times \text{SG})

values is much faster for mental arithmetic.

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Cevap

Adım Adım Çözüm

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Alternatif Yöntem

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