A 4 foot diameter pipeline carries water at a temperature of 60 F at a steady fl
ID: 1859497 • Letter: A
Question
A 4 foot diameter pipeline carries water at a temperature of 60 F at a steady flow rate of 40 cubic feet per second . The pipe line makes a 90 degree horizontal bend. The pressure at the begining of the bend is 72 pounds per square inch . The pressure at the end of the bend is 70 pounds per square inch . Determine the horizontal components of the forces necessary to hold the bend in place.
Please only answer if your sure , i will lose alot of grade points if not sure , have to solve in ft no conversions , and please show all steps and calculations.
Explanation / Answer
As the pipe is in bent in horizantal direction ,
To hold the bend it has to counter the forces in x and z direction which are in the same place.
consider x - direction
pressure force due to inlet + Fx = repulsive force due to water jet
P1A1 + Fx = -density * A1 * V1 ^2 { as the bent is of angle 90 degrees no need to consider the oulet forces as cos 90 = 0 }
Q = A1 V1 = 3.14 * 4 ^2 /4 * V1 = 40 => V1 = 3.184 foot/s
Fx = -62.4 * 3.14 * 4 ^2 /4 * 3.184 ^2 + 72 * 144 * 3.14 * 4 ^2 /4 { psi can be converted to pounds per square foot by a conversion factor of 144 and density of water =62.4 in fps system}
Fx= -7949 +130222.1= 122.273 k lbF
Consider z direction
P2A2 + Fz = -density * A2 * V2^2
Fz = -62.4 * 3.14 * 4 ^2 /4 * 3.184 ^2 + 70 *144*3.14 *4^2/4 = -7949 +126604 =118.655 klbF