Concept explainers
The variation of velocity with time.
The graph between the variations of velocity with time.
Time taken by ball to reach
Answer to Problem 111P
The time taken to reach
The graph between the variations of velocity with time is.
Explanation of Solution
Given information:
The diameter of the ball is
The below figure represent the free body diagram of the ball.
Figure-(1)
Write the expression of net force acting on the ball.
Here, the weight of the ball is
Write the expression of weight of the ball.
Here, the mass of the ball is
Write the expression of bouncy force.
Here, the mass of the fluid is
Substitute
Write the expression of the mass of the ball.
Here, the density of the ball is
Write the expression of the mass of the fluid.
Here, the density of the fluid is
Substitute
Write the expression of net force by Newton's law of motion.
Here, the acceleration is
Write the expression of acceleration.
Here, the change of velocity with respect to time is
Substitute
Substitute
Write the expression of volume of the ball.
Here, the diameter of the ball is
Write the expression of drag force by using strokes equation.
Here, the dynamic viscosity is
Substitute
Integrate Equation (VI) on both sides as initial velocity is
Substitute
Calculation:
Substitute
Substitute
Substitute
The time taken to reach
Substitute
The variation of velocity with time.
Time | Velocity |
The graph between the variation of velocity with time is.
Figure-(2)
Conclusion:
The time taken to reach
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Chapter 11 Solutions
Fluid Mechanics: Fundamentals and Applications
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