A 45o reducing elbow can be found in many piping systems. Crude oil (r = 52.5 lbm/ft3) flows into the elbow with a velocity of 5.5 ft/s and is deflected through an angle of 45o. The inlet diameter is 6-in, and the outlet diameter is 4-in. The inlet and outlet gage pressures are 35 psig and 32.5 psig, respectively. If the elbow is located in a horizontal plane, determine the restraining forces in the x and y-directions in lb

the restraining forces in the x and y-directions are :

Explanation:

From the given information;

Let us first calculate the outlet velocity by using continuity equation.

where;

= inlet diameter = 6 - In

outlet diameter = 4 -In

inlet velocity

outlet velocity = ???

 to In; we have

Since 1 ft = 12 inches; thus

12.375 ft/s = (12.375 × 12 ) inches = 148.5 In/s

5.5 ft/s =  66 In/s

By using the linear momentum  in x-direction for the  volume ; we have the relation:

where;

Therefore; the restraining forces in the x and y-directions are :