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

Answer:

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

Step-by-step explanation:

Detailed explanation and calculation is shown in the image below

Answer 2

Answer:

a) $P=312.5 lb/ft^{2}$    

b) $F=4687.5 lb$  

c) $F=843.75 lb$

Step-by-step 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:

$F=\int^{3}_{0}P*dA=\int^{3}_{0}\delta x*3dx=3\delta\int^{3}_{0}xdx=3\delta*\frac{x^{2}}{2}|^{3}_{0}=3\delta(\frac{3^{2}}{2})$

$F=3*62.5*(\frac{3^{2}}{2})=843.75 lb$

I hope it helps you!