Question

An aquarium 5 ft long, 3 ft wide, and 5 ft deep is full of water. (Recall that the weight density of water is 62.5 lb/ft3.) (a) Find the hydrostatic pressure on the bottom of the aquarium. lb/ft2 (b) Find the hydrostatic force on the bottom of the aquarium. lb (c) Find the hydrostatic force on one end of the aquarium. lb

Answer 1

a) hydrostatic pressure at bottom = 10054.375 lb/ft-s2

b) hydrostatic force at bottom = 150815.625 lb-ft/s2

c) hydrostatic force at one end of aquarium = o

Explanation:

Detailed explanation and calculation is shown in the image below

Answer 2

a)
`P=312.5 lb/ft^(2)`

b)
`F=4687.5 lb`

c)
`F=843.75 lb`

Explanation:

a) The hydrostatic pressure equation is given by:

`P=\rho gd=\delta d`

• ρ is the weight density of water (ρ = 62.5 lb/ft³)
• d is the deep of the aquarium (d = 5 ft)

So P will be:

`P=62.5*5=312.5 lb/ft^(2)`

b) The hydrostatic force of the bottom of the aquarium will be:

`F=P*A=P*(long*wide)`

`F=P*(long*wide)=312.5*5*3`

`F=4687.5 lb`

c) Here we first need to find the horizontal slice of with dx and ad deep x.

The area of this strip is: dA = 3*dx.

So the force will be:

`F=\int^(3)_(0)P*dA=\int^(3)_(0)\delta x*3dx=3\delta\int^(3)_(0)xdx=3\delta*(x^(2))/(2)|^(3)_(0)=3\delta((3^(2))/(2))`

`F=3*62.5*((3^(2))/(2))=843.75 lb`

I hope it helps you!