Answer to Question #191400 in Molecular Physics | Thermodynamics for Arthur Paul

Question

1. A jet of water moving at a velocity of 30m/s impinges on a series of vanes moving at 15 m/s. The jet makes an angle 30^o to the direction of motion of vanes at entry and leaves the vanes at 60^o. Draw the inlet and outlet velocity diagrams and find i) vane angles at inlet and outlet ii) work done per second per Newton of water, and iii) hydraulic efficiency

Answer 1

$v_1=30~\frac ms,~ v_2=15~\frac ms,~ \alpha=30°,~\beta=180°-60°=120°.$

1.

$v_w=v_1\cos \alpha=25.98~\frac ms,$

$v_s=v_1\sin \alpha=15~\frac ms,$

$v_b=v_w-v_2=10.98~\frac ms,$

$v_r=\sqrt{v_b^2+v_s^2}=18.59~\frac ms,$

$\theta=\arctan \frac{v_s}{v_b}=53.8°,$

$\frac{v_r}{\sin(180°-\beta)}=\frac{v_2}{\sin(\beta-\psi)},$

$\psi=75.67°,$

$v_f=v_r\cos\psi-v_2=-10.4~\frac ms,$

2.

$W=\frac{(v_w+v_f)v_2}{g}=23.82~Nm/N ~weight~ of ~water,$

3.

$\eta=\frac{2(v_w+v_f)v_2}{v_1^2}=0.52=52\%.$