
(a)
Estimate the minimum length of the tank if the particle diameter is equal to

Answer to Problem 7.72P
Explanation of Solution
Given information:
The depth of the water tank is
The velocity of water flow is
The specific gravity of tank material is
The Newton’s law of downward motion is defined as,
Where,
The buoyancy force is defined as,
The drag force is defined as,
In above equation,
Calculation:
The horizontal velocity
Assume vertical velocity as
Apply Newton’s law of downward motion,
The weight of the sphere
Therefore,
Calculate the weight of the sphere,
Calculate the Buoyancy force exerted on sphere,
Substitute in equation (1),
Solve for
The length of the tank can be defined as,
Where,
According to the definitions, we can assume,
Therefore,
Find vertical velocity,
Calculate the minimum length of the tank,
Conclusion:
The minimum length of the tank if
(b)
Estimate the minimum length of the tank if the particle diameter is equal to

Answer to Problem 7.72P
Explanation of Solution
Given information:
The depth of the water tank is
The velocity of water flow is
The specific gravity of tank material is
The Newton’s law of downward motion is defined as,
Where,
The buoyancy force is defined as,
The drag force is defined as,
In above equation,
Calculation:
According to sub-part a,
We can say,
The length of the tank can be defined as,
Where,
According to the definitions, we can assume,
Therefore,
Find vertical velocity,
Calculate the minimum length of the tank,
Conclusion:
The minimum length of the tank if
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Chapter 7 Solutions
Fluid Mechanics
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