7 Two fluid jets are pointed at surfaces as shown in the fol

7) Two fluid jets are pointed at surfaces as shown in the fol lowing figures. The fluids are incompressible, and the effects of gravity can be neglected. The mass flowrates and the velocities of the jets are identical. The cross-sectional areas of the jets do not change significantly as the fluid flows 110 points] The correct statement regarding the horizontal forces is a) Fi equals 2 F b) F, is greater than o hd F, equals o c) F, equals F,/2. d) F, equals O and F e) Fi equals F xreater than O. Surface Nozzle 2 Flu d stream Nozzle Fluid stream Surface

Solution

Ans. we can solve this by following procedure

To get the relation first we need to get force applied.

the force applied by the plate on the jet to change the direction of jet is change in momentum of jet.

we need to equate the forces in horizontal direction in both the cases to get relation.

For Case 1:

change in momentum of the jet = m^. (V - (-V)) = 2 m^.V (As given the change in velocity is Zero)

m^. = Mass flow rate of fluid kg/s

V = Velocity of jet in Horizontal direction, m/s

change in momentum = 2 m^.V

Equate horizontal forces F₂ = 2 m^.V ----(Equation 1)

For Case 2:

change in momentum of the jet = m^. (V - 0) = m^.V (At exit there is no velocity in horizontal direction)

m^. = Mass flow rate of fluid kg/s

V = Velocity of jet in Horizontal direction, m/s

change in momentum in case 2 = m^.V

Equate horizontal forces F₁ = m^.V ----(Equation 2)

Equate Equation 1 and 2

we get F₂ = 2. F₁

F₁ = F₂ / 2