Concept explainers
An incompressible fluid of density
FIGURE P6-47
(a)
The expression for the horizontal force.
Answer to Problem 47P
The expression for the for the horizontal force is
Explanation of Solution
Given information:
The area at inlet is
Write the expression for the mass flow rate at inlet.
Here, the density of fluid is
Write the expression for the mass flow rate at inlet.
Here, the velocity at exit is
Since mass neither be created nor be destroyed, therefore, mass flow rate at inlet and exit will be same
Write the expression for the conservation of mass.
Write the expression for the moment Equation.
Here, the horizontal force is, the pressure at inlet is
Write the expression for the component of exit velocity along the horizontal direction.
Write the expression for the component of exit pressure along the horizontal direction.
Here, the pressure at exit is
Substitute
Conclusion:
The expression for the for the horizontal force is
(b)
The value for the horizontal force.
Answer to Problem 47P
The value for the horizontal force is
Explanation of Solution
Given information:
The area at inlet is
Write the expression for the mass flow rate at inlet.
Here, the density of fluid is
Write the expression for the mass flow rate at inlet.
Here, the velocity at exit is
Since mass neither be created nor be destroyed, therefore, mass flow rate at inlet and exit will be the same.
Write the expression for the conservation of mass.
Write the expression for the moment equation.
Here, the horizontal force is, the pressure at inlet is
Write the expression for the component of exit velocity along the horizontal direction.
Write the expression for the component of exit pressure along the horizontal direction.
Here, the pressure at exit is
Substitute
Calculations:
Substitute
Substitute
Substitute
Conclusion:
The value for the horizontal force is
(c)
The turning angle at which force is minimized.
Answer to Problem 47P
The turning angle at which force is minimized is
Explanation of Solution
Given information:
The area at inlet is
Write the expression for the mass flow rate at inlet.
Here, the density of fluid is
Write the expression for the mass flow rate at inlet.
Here, the velocity at exit is
Since mass neither be created nor be destroyed, therefore mass flow rate at inlet and exit will be same
Write the expression for the conservation of mass.
Write the expression for the moment equation.
Here, the horizontal force is, the pressure at inlet is
Write the expression for the component of exit velocity along the horizontal direction.
Write the expression for the component of exit pressure along the horizontal direction.
Here, the pressure at exit is
Substitute
Write the expression for the maximum turning angle.
Differentiate Equation (V) with respect to turning angle.
Since
Substitute
Calculations:
Substitute
Since
Conclusion:
The turning angle at which force is minimized is
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Chapter 6 Solutions
Fluid Mechanics Fundamentals And Applications
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