The water is flowing in a cylindrical pipe of radius 1 inch. Because water is viscous and sticks...

Question:

Water is flowing in a cylindrical pipe of radius 1 inch. Because water is viscous and sticks to the pipe, the rate of flow varies with the distance from the center. The speed of the water at a distance {eq}r {/eq} inches from the center is {eq}10(1-r^2) {/eq} inches/second. What is the rate (in cubic inches per second) at which water is flowing through the pipe?

Discharge

It represents the rate at which the volume of given fluid passes through a pipe or a hole. It depends on the velocity by which fluid flows and the area of the pipe. It represented by SI unit {eq}m^3/s {/eq}

Answer and Explanation:

Given Data

  • Equation of speed is, {eq}v = 10\left( {1 - {r^2}} \right) {/eq}

As the cross-section of pipe is circular,

The expression of area of...

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