Question

Please show all work.

3 Above is pictured a large tank that is ejecting fluid from a nozzle into a free jet of fluid that strikes a yane. The vane is attached to 2 springs that resist the motion of the vane due to the striking fluid, and the vane's orientation remains the same (i.e. there is no angular deflection) At point 2 the free jet has a diameter of D2 and at point 3 the free jet has a diameter of Dj. The flow is steady state and the free jet enters and exits the vane with 1D flux. The heights of the tank and the vane are known as are density ρ and viscosity μ. a) Find the velocity of the fluid at point 2. b) Find the deflection of both springs due to the fluid in terms of known parameters Hh, D2

Answer 1

Applying Bernoulli Therom:

con s P1 = P2

Conservation of mass at 2 and 3, we get:

Now rate of change of momentum is force applied on spring k = px 3.14 × D:14 × 2g(h1-h2) kx Now rate of change of momentum is force applied on spring ky De flection(x) x 3.14 x D/4 x 2g(hi - h2 × 3.14 × D3/4 × 2g(h1-h2) Deflection(y)