# Find the work in pumping the water out fo the tank

• Punkyc7
In summary, the conversation discusses the calculation of work required to pump water out of a bowl-shaped tank with a radius of 2 inches and filled with water to a depth of 1 inch. The formula W=FD is used, where F is equal to the density of water (rho) multiplied by the volume (V). The volume is calculated by integrating the surface area multiplied by the height, with the limits from 0 to 1. However, there is confusion about the limits as the water level changes from 1 to 2, with the distance from the center top surface of the bowl being measured.
Punkyc7
a bowl shaped tank is in the shaoe of a hemisphere with a radius of 2 in. If the bowl is filled with water density rho to a depth of 1 in, find the work in pumping the water out fo the tank

W=FD

V=integral of surface area * height

F= rho *V
V is the integral of pi(r-x)^2 from 0-1
D=2-x

so W=rho*V int 2-x from 0-1

i get 7pi rho g/2 and the answer is suppose to be 9 rho pi/4

im not sure where i am going rong but i thing it has to do with my integration

we haven't done parametrics yet

dV = π*r^2*dh.

r^2 = R^2 - h^2.

Hence V = π*Int[R^2 - h^2]*dh from h = 1 to h = 2.

Now proceed.

I think the answer is wrong.

Why are your limits from 1-2 its only filled half way shouldn't it be 0-1 if your point of reference is from the bottm

Punkyc7 said:
Why are your limits from 1-2 its only filled half way shouldn't it be 0-1 if your point of reference is from the bottm
While emptying the bowl, water level changes from 1 to 2, where h is measured from the center. When you write down the relation between R and h, h is measured from the center top surface of the bowl.

ah ok i was doing it from the bottom so the distance is 1 + x now right

## 1. How do you calculate the work required to pump water out of a tank?

The work required to pump water out of a tank can be calculated using the formula W = mgh, where W is the work in joules, m is the mass of the water being pumped, g is the acceleration due to gravity, and h is the height the water needs to be pumped to.

## 2. What factors affect the amount of work required to pump water out of a tank?

The amount of work required to pump water out of a tank is affected by the height the water needs to be pumped to, the mass of the water being pumped, the efficiency of the pump being used, and the force of gravity.

## 3. How does the height of the tank affect the amount of work required to pump water out?

The height of the tank directly affects the amount of work required to pump water out. The higher the tank, the more work is required to pump the water to the desired height due to the increased potential energy of the water.

## 4. Can the efficiency of the pump affect the amount of work required to pump water out of a tank?

Yes, the efficiency of the pump can affect the amount of work required. A more efficient pump will require less work to pump the same amount of water compared to a less efficient pump.

## 5. Is the mass of the water being pumped a significant factor in calculating the work required?

Yes, the mass of the water being pumped is a significant factor in calculating the work required. The more water that needs to be pumped, the more work is required to overcome the force of gravity and pump it to the desired height.

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