Question

A circular plate having a diameter of 330 mm is held perpendicular to an axisymmetric horizontal jet of air having a velocity of 43 m/s and a diameter of 88 mm as shown in the figure below. A hole at the center of the plate results in a discharge jet of air having a velocity of 43 m/s and a diameter of 22 mm. Determine the horizontal component of force required to hold the plate stationary.

F =

N

the tolerance is +/-2%

Answer 1

Ans) The control volume contains the plate and flowing air. So,use equilibrium condtion and equate forces in horizontal direction to zero,

=> - 1 A1 +  2 A2 + Fx = 0

=> Fx =  1 A1 - 2 A2

Also, A1 = Area of larger pipe = (/4)() = 0.00608

A2 = Area of smaller pipe = (/4)() = 0.00038

V1 = V2 = 43 m/s

1 = 2 = Density of air = 1.23 kg/

Putting values,

=> Fx = (1.23 x 0.00608 x 43 x 43) - (1.23 x 0.00038 x 43 x 43)

=> Fx = 13.827 - 0.864

=> Fx = 12.963 N

Hence, horizontal component of force to hold plate stationary is 12.963 N