Force Exerted on a Reducing Bend

Example 1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity Vl is given and the pressures pl and p. are measured. Selecting the inlet and outlet surfaces 1 and 2 as shown, the continuity equation Eq. (6-9) can be used to find the exil velocity Vz = VjA/A. The mass flow rate is obtained by m = p V. A.  

Assume that the velocity profile is nearly uniform so that (1 is approximately unity. The force exerted on the fluid by the bend has x and y components these can be found from Eq. (6-11). The x component gives 

The force acting on the fluid is F the equal and opposite force exerted by the fluid on the bend is —F. 

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Example 1 Force Exerted on a Reducing Bend An incompressible fluid flows through a reducing elbow (Fig. 6-5) situated in a horizontal plane. The inlet velocity Vj is given and the pressures pi and measured. 

A 90° horizontal reducing bend has an inlet diameter of 4 in. and an outlet diameter of 2 in. If water enters the bend at a pressure of 40 psig and a flow rate of 500 gpm, calculate the force (net magnitude and direction) exerted on the supports that hold the bend in place. The loss coefficient for the bend may be assumed to be 0.75 based on the highest velocity in the bend. 

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