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An aquarium 5 ft long, 2 ft wide and 3 ft deep is full of water. a. Find the hydrostatic pressure...

Question:

An aquarium 5 ft long, 2 ft wide and 3 ft deep is full of water.

a. Find the hydrostatic pressure on the bottom of the tank.

b. Find the hydrostatic force at the bottom of the tank.

c. Find the hydrostatic force on one end of the aquarium.

Rectangle:

A rectangle is a special type of parallelogram. The rectangle has each angle of 90 degree and diagonals are equal, and the area of the rectangle is equalled to the product of length and width.

Answer and Explanation:

Given,

Length (l)=5ft

Wide (w)=2ft

Depth (d)=3ft

The weight density of water is {eq}62.5\;{\rm{lb/f}}{{\rm{t}}^{\rm{3}}} {/eq}

(A) The hydrostatic pressure on the bottom of the tank is

Pressure =density of water *depth

{eq}\begin{align*} p &= \delta \times d\\ p &= 62.5 \times 3\;{\rm{lb/f}}{{\rm{t}}^{\rm{2}}}\\ &= 187.5\;{\rm{lb/f}}{{\rm{t}}^{\rm{2}}} \end{align*} {/eq}

(B) The hydrostatic force at the bottom of the tank is

Force = area * pressure

{eq}F = A \times P {/eq}

area = length *width

{eq}\begin{align*} A &= {\rm{5 \times 2\;f}}{{\rm{t}}^{\rm{2}}}\\ &= 10\;{\rm{f}}{{\rm{t}}^{\rm{2}}} \end{align*} {/eq}

And put the value,

{eq}\begin{align*} F &= 10 \times 187.5\;{\rm{f}}{{\rm{t}}^{\rm{2}}} \times {\rm{lb/f}}{{\rm{t}}^{\rm{2}}}\\ &= 1875\;{\rm{lb}} \end{align*} {/eq}

(C) The hydrostatic force on one end of the aquarium is

Force =pressure * area

Force on each strip = (4-x)

{eq}\begin{align*} P &= 62.5 \times 4\\ &= 250\;{\rm{lb/f}}{{\rm{t}}^{\rm{2}}} \end{align*} {/eq}

{eq}\begin{align*} F &= \int_0^4 {250\left( {4 - x} \right)dx} \\ &= 250\int_0^4 {\left( {4 - x} \right)dx} \\ &= 250\left[ {4x - \dfrac{{{x^2}}}{2}} \right]_0^4\\ &= 250\left[ {\left( {4 \times 4 - \dfrac{{{4^2}}}{2}} \right) - 0 - 0} \right]\\ &= 250\left[ {16 - \dfrac{{16}}{2}} \right]\\ & = 250\left( {\dfrac{{32 - 16}}{2}} \right)\\ &= 250 \times \dfrac{{16}}{2}\\ &= 250 \times 8\\ &= 2000\;{\rm{lb}} \end{align*} {/eq}

(A) Pressure = {eq}187.5\;{\rm{lb/f}}{{\rm{t}}^{\rm{2}}} {/eq}

(B) Force = {eq}1875\;{\rm{lb}} {/eq}

(C) Force = {eq}2000\;{\rm{lb}} {/eq}

.


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