A rectangular tank that is L m long, W m wide and H m deep is full of water. Fin

Question

A rectangular tank that is L m long, W m wide and H m deep is full of water. Find the work needed to pump half of the water out of the tank. (Use the fact that the density of water is 1000 kg/m3.)

If L=4 m, W=2m and H=6m,

(a) find the work needed to pump all of the water out of the tank.

b) find the work done to pump half of the water out of the tank.

A rectangular tank that is L m long, W m wide and H m deep is full of water. Find the work needed to pump half of the water out of the tank. (Use the fact that the density of water is 1000 kg/m3.) W = b a F(x)dx If L=4 m, W=2m and H=6m, find the work needed to pump all of the water out of the tank. find the work done to pump half of the water out of the tank.

Explanation / Answer

W = Change in energy of system

For pumping all water, change in Energy = m*g*delta(h)

delta(h) = COM of water

W = 1000*(4*2*6)*9.81*(6+0)/2 = 1,412,640 j

For the top half of water, Energy = m*g*h

delta(h) = COM of top half of water

W = 1000*(4*2*3)*9.81*(6+3)/2 = 1,059,480 J

a) Force = constant = m*g

'int' stands for integration

W = int( - F.dx) = -F. int (dx) | x=3 to x=0

(Force = -F, because force and displacement are opposite direction)

-F.x| x=3 to x=0 = m_total*g*(3) =1,412,640 J

b) Force = constant

'int' stands for integration

W = int(- F.dx) = -F. int (dx) | x=6 to x=1.5   

-F.x| x=6 to x=1.5

= m_half * g*(4.5) = 1,059,480J

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