Concept explainers
Water flows at mass flow rate m through a 90° vertically oriented elbow of elbow radius R (to the centerline) and lime, pipe diameter D as sketched. The outlet s exposed to the atmospheric. (Hint: This means that the pressure at the outlet is atmospheric pressure.) The pressure at the inlet must obviously be higher than atmospheric in order to push the water through the elbow and to raise the elevation of the water. The irreversible head loss through the elbow is hL. Assume that the kinetic energy flux correction factor a is not unity, but is the same at the inlet and outlet of the elbow
(a) Using the head form of the energy equation, derive an expression for the gage pressure
(b) Plug in these numbers and solve for
(c) Neglecting the weight of the elbow itself and the weight of the water in the elbow, calculator the x and z components of the anchoring force required to hold the elbow in place. Your final answer for the anchoring force should be given as a
(d) Repeat Part (c) without neglecting the weight of the water in the elbow. Is it reasonable to neglect the weight of the water in this problem?
(a)
The expression of gage pressure using the head form of energy equation.
Answer to Problem 96P
The expression of gage pressure is
Explanation of Solution
Given information:
The elbow is
Write the expression of Bernoullis equation at inlet and outlet of elbow pipe.
Here, the pressure at inlet is
Write the expression of gage pressure.
Here, the inlet pressure is
Consider, the velocity of flow at inlet and outlet is same i.e.
Substitute,
Substitute
Conclusion:
The expression of gage pressure is
(b)
The gage pressure.
Answer to Problem 96P
The gage pressure is
Explanation of Solution
Given information:
The density of the fluid is
Calculation:
Substitute
Conclusion:
The gage pressure is
(c)
The
Answer to Problem 96P
The
The
Explanation of Solution
Given information:
Neglect the weight of elbow and weight of the water.
Write the expression of
Here, the momentum flux correction factor is
Substitute,
Write the expression of
Here, the momentum flux correction factor is
Substitute
Write the expression of mass flow rate of fluid.
Here, the density of the fluid is
Write the expression of area of flow.
Here, the diameter of the pipe is
Calculation:
Substitute
Substitute
Substitute
So, the force is acting on opposite direction.
Substitute
Conclusion:
The
The
(d)
The
Answer to Problem 96P
The
The
Explanation of Solution
Given information:
The weight of water in the elbow is considered.
Write the expression of
Here, the momentum flux correction factor is
Substitute,
Write the expression of
Here, the momentum flux correction factor is
Substitute
Write the expression of weight of water in the elbow.
Here, the mass of water is
Write the expression of mass of water.
Here, the density of the fluid is
Write the expression of volume of water.
Here, the area of flow is
Calculation:
Substitute
So, the force is acting on opposite direction.
Substitute
Substitute
Substitute
Substitute
Conclusion:
The
The
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Chapter 6 Solutions
Fluid Mechanics: Fundamentals and Applications
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