(a)
The validation of continuity equation.
Answer to Problem 4.30P
The continuity equation is valid for the given velocity distribution.
Explanation of Solution
Given information:
Two dimensional converging nozzle velocity distribution in
Write the expression for two dimensional incompressible continuity Equation.
Here, the velocity of fluid along
Calculation:
Substitute
Conclusion:
The given distribution satisfies the two dimensional continuity equation..
(b)
The validation of Navier stokes equation.
Answer to Problem 4.30P
Navier stokes equation is valid for the the given velocity distribution.
Explanation of Solution
Write the expression for two dimensional incompressible Navier stoke equation in
Write the expression for two dimensional incompressible Navier stoke equation in
Here, the velocity of fluid along
Write the expression for validation for Navier stokes equation in x-direction.
Write the expression for validation for Navier stokes equation in y-direction.
Calculation:
Substitute
Substitute
Substitute
Hence the equation
Substitute
Hence the equation
Conclusion:
Navier stokes equation is valid for the given velocity distribution.
(c)
The pressure distribution
Answer to Problem 4.30P
The pressure distribution
Explanation of Solution
Given information:
The pressure at the origin is
Write the expression for pressure distribution in
Write the expression for pressure distribution in
Write the expression for pressure distribution
Calculation:
Substitute
Substitute
Substitute
Substitute
Conclusion:
The pressure field
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Chapter 4 Solutions
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