How to Calculate the Work Required to Pump Fuel from a Tank

To calculate the work required to pump the fuel, we first need to find the total height the fuel needs to be pumped, which is the sum of the tank height and the additional height of 13 ft. Therefore, the total height is 8 ft + 13 ft = 21 ft.

Next, we calculate the area of the cross-section of the tank, which is a right-circular cylinder. The formula for the area of a circle is πr², where the radius (r) of the tank is 4 ft. Substituting the value of the radius into the formula, we get the area of the cross-section as 16π ft².

Now, we use the formula for work done in pumping the fuel, which is represented as an integral. The work done required is given by the integral of the product of the weight of the fuel, the area of the cross-section, and the pumping distance from 0 to 8 ft (the height of the tank) to pump all the fuel. Therefore, the equation to calculate the work done is:

Work = ∫[0, 8] 52 x 16π (21 - y) dy

After calculating the integral, we find that the work required to pump the fuel from the tank to a point 13 ft above the top of the tank is 355477 ft-lb.

Therefore, the amount of work needed to pump all the fuel from the tank to a point 13 ft above the top of the tank is 355477 ft-lb. This calculation considers the weight of the fuel, the dimensions of the tank, and the total distance the fuel needs to be pumped. By understanding the process and using the appropriate formulas, we can accurately determine the work required in such scenarios.