in a vertical plane. The axis at inlet is horizontal and the centre of the outlet section is 1.5 m below the centre of the inlet section. Total volume of water in the bend is 0.9 m'. Neglecting friction, calculate the magnitude and direction of the force exerted on the bend by water flowing through it at 250 litress and when inlet pressure is 0.15 N/mm”.

Given: angle of bend θ=$120^{\circ}$

Diameter of pipe at inlet $D_{1}$=30cm=0.30m

Diameter of pipe at outlet $D_{2}$=15cm=0.15m

Area at inlet , $A_{1}=\frac{π}{4} D1^{2}=0.0706m^2$

Area at outlet, $A_{2}=\frac{π}{4} D_2^{2}=0.01767m^2$

Pressure at inlet =$0.15N⁄mm^{2} =0.14×10^6 N⁄m^2 $

Q=250litres/sec=$0.25m^{3}sec$

$z_{2}$=-1.5m

$V_1=\frac{Q}{A_1} =\frac{.25}{.0706}$=3.541m/s

$V_2=\frac{Q}{A_2} =\frac{.25}{.01767}=14.1483m/s$

Applying Bernoulli’s equation at section 1 and 2

$\frac{p_1}{ρg}+\frac{V_1^{2}}{2g}+z_1=\frac{p_2}{ρg}+\frac{V_2^{2}}{2g}+z_2$ …