Question

A conical reservoir has an altitude of 3.6 m and its upper base radius is 1.2 m. If it is filled with a liquid of unit weight 9.4 kN/m^3 to a depth of 2.7 m, find the work done in pumping the liquid to 1.0 above the top of the tank. (Please use formula > Wf = γf hTVf

a. 55.41 kJ

b. 41.55 kJ

c. 45.15 kJ

d. 51.45 kJ

Answer 1

To find the work done in pumping the liquid above the top of the tank, we can use the formula Wf = γf hTVf, where γf is the unit weight of the liquid, hT is the total height to pump the liquid, and Vf is the volume of the liquid. The correct answer is option a. 55.41 kJ.

Step-by-step explanation:

To find the work done in pumping the liquid above the top of the tank, we can use the formula Wf = γf hTVf, where γf is the unit weight of the liquid, hT is the total height to pump the liquid, and Vf is the volume of the liquid.

The volume of the liquid is given by the formula Vf = (1/3)πr^2h, where r is the radius of the tank's upper base and h is the height of the liquid. We can calculate the volume of the liquid in the tank.

Then, we can calculate the work done using the given values of γf and hT. The correct answer is option a. 55.41 kJ.

Answer 2

To find the work done in pumping the liquid to 1.0 m above the top of the tank, we can use the formula Wf = γf hTVf. By substituting the given values into the formula and performing the necessary calculations, we find that the work done is approximately 481.17 kJ.

Step-by-step explanation:

To calculate the work done in pumping the liquid to 1.0 m above the top of the tank, we can use the formula Wf = γf hTVf, where Wf is the work done, γf is the unit weight of the liquid, hT is the total height the liquid is pumped, and Vf is the volume of the liquid.

First, let's find the volume of the liquid. The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone. Substituting the given values, we have V = (1/3)π(1.2m)^2(2.7m) = 8.16 cubic meters.

Next, we need to calculate the total height the liquid is pumped. The total height is equal to the depth of the liquid plus the altitude of the cone. So, hT = 2.7m + 3.6m = 6.3m.

Now we can calculate the work done. Substituting the values into the formula, we have Wf = (9.4 kN/m^3)(6.3m)(8.16 cubic meters) = 481.1744 kJ.

Rounding the answer to two decimal places, the work done in pumping the liquid is approximately 481.17 kJ.