# Time to Empty a Tank with Water Flowing at 2h kg/s

• Manshah
In summary, a tank with a radius of 10 meters and filled with water up to its brim has a hole at the bottom. The time taken for the tank to empty completely, with water flowing out at a rate of 2h kg/s, can be calculated using the differential equation for change of mass in the tank. The equation takes into account the density of water, the horizontal cross section area, and a constant to adjust physical dimensions.
Manshah
a tank is filled with water up to its brim a hole was made at the bottom of tank find time taken to empty tank if water flows at rate of 2h kg/s where h is height of liquid column and is equal to 20m radius is equal to h/2

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Differential equation for change of mass in the tank for infinitesimal time change dt is
$$\rho dV=\rho Adh =-2h c dt$$
where ##\rho## is density of water ##1000 kg/m^3##, A is horizontal cross section area ##2*20*\pi ##m^2, c is constant to adjust physical dimension c = 1 kg /(sec meter). h=40 m when t=0.

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## 1. How is the time to empty a tank calculated?

The time to empty a tank is calculated by dividing the volume of water in the tank by the rate of water flow. This will give you the time it takes for the tank to completely empty.

## 2. What is the formula for calculating the time to empty a tank?

The formula for calculating the time to empty a tank is: Time = Volume of Water / Rate of Water Flow

## 3. Can the time to empty a tank be affected by the size of the tank?

Yes, the time to empty a tank can be affected by the size of the tank. A larger tank will take longer to empty compared to a smaller tank with the same rate of water flow.

## 4. How does the rate of water flow impact the time to empty a tank?

The rate of water flow directly affects the time to empty a tank. The higher the rate of water flow, the faster the tank will empty. Similarly, a lower rate of water flow will result in a longer time to empty the tank.

## 5. What units should be used for the rate of water flow and volume of water?

The rate of water flow should be measured in kilograms per second (kg/s) and the volume of water should be measured in liters (L) or cubic meters (m^3). It is important to use consistent units when calculating the time to empty a tank.

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