Question

Water enters a 180° elbow with an average velocity V1 = 3 m/s. The diameter at the inlet of the elbow is 6.0 cm and the exit diameter is 2.0 cm. The water exits to atmosphere. Determine the magnitude of the horizontal force required to hold the elbow in place. (Ignore the pressure component of the force.)

Answer 1

Answer:203.60 N

Step-by-step explanation:

Given

`V_(inlet)`=3 m/s

`d_(inlet)`=6 cm

`d_(outlet)`=2 cm

Using continuity equation

`A_(inlet)V_(inlet)=A_(outlet)V_(outlet)`

`(\pi * d_(inlet)^2)/(4)* 3`=
`(\pi * d_(outlet)^2)/(4)* V_(outlet)`

`V_(outlet)`=27 m/s

Horizontal Force required to hold elbow=Change in momentum of water

initial momentum=
`\rho * A_(inlet)* V_(inlet)=10^(3)* (\pi)/(4)6^2* 3^(2)* 10^(-4)`

Final Momentum=
`\rho * A_(outlet)* V_(outlet)=10^(3)* (\pi)/(4)2^2* 27^(2)* 10^(-4)`

Force required=
`10^(3)* (\pi )/(4)* 10^(-4)\left [ 27^(2)* 2{2}-6{2}* 3{2}\right ]`=203.60 N