Question

A two-dimensional water jet strikes a fixed two-dimensional plate at 30° to the normal to the plate. This causes the jet to split into two streams in which the ratio of larger discharge to smaller discharge is

• A. 14.0
• B. 3.0
• C. 2.0
• D. 1.0

Answer 1

The correct option is B 3.0

On splitting of jet into two streams, the larger discharge would be

$Q_1=\frac{Q}{2}(1+\cos \theta )$
and, smaller discharge would be

$Q_2=\frac{Q}{2}(1-\cos \theta )$

$So,\frac{Largedischarge}{Smallerdischarge}=\frac{\frac{Q}{2}(1+\cos \theta )}{\frac{Q}{2}(1-\cos \theta )}$

$=\frac{1+\cos \theta }{1-\cos \theta }$

$=\frac{1+\cos (90{}^{\circ }+30{}^{\circ })}{1-\cos (90{}^{\circ }-30{}^{\circ })}=\frac{1+\frac{1}{2}}{1-\frac{1}{2}}=\frac{3}{1}=3$