Ask Question
7 October, 02:31

A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water. Assume that a

+4
Answers (1)
  1. 7 October, 06:01
    0
    W = 1.06 MJ

    Explanation:

    - We will use differential calculus to solve this problem.

    - Make a differential volume of water in the tank with thickness dx. We see as we traverse up or down the differential volume of water the side length is always constant, hence, its always 8.

    - As for the width of the part w we see that it varies as we move up and down the differential element. We will draw a rectangle whose base axis is x and vertical axis is y. we will find the equation of the slant line that comes out to be y = 0.5*x. And the width spans towards both of the sides its going to be 2*y = x.

    - Now develop and expression of Force required:

    F = p*V*g

    F = 1000 * (2*0.5*x*8*dx) * g

    F = 78480*x*dx

    - Now, the work done is given by:

    W = F. s

    - Where, s is the distance from top of hose to the differential volume:

    s = (5 - x)

    - We have the work as follows:

    dW = 78400*x * (5-x) dx

    - Now integrate the following express from 0 to 3 till the tank is empty:

    W = 78400 * (2.5*x^2 - (1/3) * x^3)

    W = 78400 * (2.5*3^2 - (1/3) * 3^3)

    W = 78400*13.5 = 1058400 J
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers