A reducing elbow in a horizontal pipe is used to deflect water flow by an angle θ = 45° from the flow direction while accelerati
ng it. The elbow discharges water into the atmosphere. The cross- sectional area of the elbow is 150 cm2 at the inlet and 25 cm2 at the exit. The elevation difference between the centers of the exit and the inlet is 40 cm. The mass of the elbow and the water in it is 50 kg. Determine the anchoring force needed to hold the elbow in place. Take the momentum flux correction factor to be 1.03 at both the inlet and outlet.
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We can solve the problem by using the first law of thermodynamics:
where
is the variation of internal energy of the system
Q is the heat added to the system
W is the work done by the system
In this problem, the variation of internal energy of the system is
While the heat added to the system is
therefore, the work done by the system is