Question 5.11: A jet of water issuing from a stationary nozzle with a unifo...
A jet of water issuing from a stationary nozzle with a uniform velocity, V, strikes a frictionless turning vane mounted on a cart, as shown in Fig. 5.13. The vane turns the jet through an angle \theta. The area corresponding to the jet velocity, V, is A. An external mass, M, is connected to the cart through a frictionless pulley. Determine the magnitude of M required to hold the cart stationary. Assume the ground to be frictionless.
Choose a fixed CV, as shown by the dashed line in Fig. 5.13(a).
Applying the x component of the linear momentum equation to the inertial CV, we have
F_{x}=\int_{A} \rho \vec{V}(\vec{V} \cdot \hat{n}) d A=\rho V \cos \theta(A V)+\rho(V)(-A V)=-T (5.28)
where T is the tension the string (see Fig. 5.13(b), which shows forces acting on the CV).
T=\rho A V^{2}(1-\cos \theta)Since, for equilibrium, tension in the string equals to Mg, because of frictionless nature of the pulley, we have
T=\rho A V^{2}(1-\cos \theta)=M gOr M=\frac{\rho A V^{2}(1-\cos \theta)}{g} (5.29)
