Question

V cart Nozzle V. jet- 4. (20 pts) A 3-cm-diameter water jet moving at 40 m/s velocity in x-direction strikes the vertical back surface of a cart moving horizontally at a constant speed of 10 m/s in the flow direction. After the strike, the water stream splatters off in all directions in the plane of the back surface. Using the moving control volume indicated with dashed lines in the figure, determine: Waterjeti F. Rx X a) The relative velocity and mass flow rate of the jet in control volume. b) The force that needs to be applied by the brakes of the cart to prevent it from accelerating. c) The relative velocity of the jet in control volume if the cart is moving at 10 m/s in negative x-direction. d) The force that needs to be applied by the brakes of the cart to prevent it from accelerating for the above case c. Note that for control volumes that move with velocity V cv valid: , the momentum equation is EF=XB,^,V,-EB,m,V, out in where V,=V - cv is the relative velocity, m, is calculated using the relative velocity. Take pw=1000 kg/mº.

Answer 1

As the water flows out of control volume along the plane of the back surface, the exit velocity component in x-direction is zero. So, only the inlet relative velocity is responsible for thrust force. Using this, the brake forces are obtained as shown in the attached images.

Solution: Jet diameter = 3 cm -0.03 m Jet's absolute relocity = 40 mlo 10 mls. Veart - Vjet velocity of Cart Consider velocities in positive direction be positive as well V cart Vjet the Taking as control volume given, we have : Cv i) Relative velocity of jet in control volume Vonel V get av Cart 40 - 10 130 m/) ii) mass flow rate of jet m density x volume flow rate = 8 fx (A Vered) - 1 x 2 a ²) (Vrel) 1000 x 5 0.0%) ² (30) 21.206 Kg/sec is equal to the b) The force to be be applied by brakes thrust force applied by the jet on the back Cart surface of the