A municipal water treatment facility utilizes two open-air settling basins with flat botto… — Armed Services Vocational Aptitude Battery (ASVAB)

A municipal water treatment facility utilizes two open-air settling basins with flat bottoms. Basin Alpha is a wide rectangular pool with a base area of $50\text{ m}^2$ , currently holding $150\text{ m}^3$ of water. Basin Beta is a narrow cylindrical well with a base area of $5\text{ m}^2$ , currently holding $30\text{ m}^3$ of water. What is the ratio of the gauge hydrostatic pressure exerted on the bottom of Basin Alpha to the gauge hydrostatic pressure exerted on the bottom of Basin Beta?

$1:2$ Answer
B
$5:1$
C
$10:1$
D
$2:1$

Answer

The ratio is

1:2

, because gauge hydrostatic pressure depends exclusively on the vertical depth of the fluid, which is

3\text{ m}

in Basin Alpha and

6\text{ m}

in Basin Beta.

Hydrostatic pressure depends exclusively on the depth of the fluid, not the total volume or the base area. The depth of the water in Basin Alpha is

3\text{ m}

(

150\text{ m}^3 / 50\text{ m}^2

). The depth in Basin Beta is

6\text{ m}

(

30\text{ m}^3 / 5\text{ m}^2

). The ratio of these depths is

3:6

, which simplifies to

1:2

Step-by-Step Solution

Calculate the depth of water in Basin Alpha.

h_{Alpha} = \frac{150\text{ m}^3}{50\text{ m}^2} = 3\text{ m}

Hydrostatic pressure is determined by fluid depth. Depth is found by dividing the total volume by the base area.

Calculate the depth of water in Basin Beta.

h_{Beta} = \frac{30\text{ m}^3}{5\text{ m}^2} = 6\text{ m}

The exact same volumetric relationship applies to find the vertical depth in the second basin.

Determine the ratio of their hydrostatic pressures.

Ratio =

3\text{ m} : 6\text{ m} = 1:2

Because both basins contain the same fluid (water) under the same gravitational force, the ratio of their bottom pressures is exactly equal to the ratio of their depths (

P = \rho g h

Key Concept

Hydrostatic pressure is completely independent of a container's shape, base area, or total fluid volume; it depends exclusively on fluid density, gravity, and vertical depth.

Estimated Time:1m 30s

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