Question

A flat plate orifice of 2 in. diameter is located at the end of a 4-in. diameter pipe. Water flows through the pipe and orifice at 2 ft3/s. The diameter of the water jet downstream from the orifice is 1.5 in. Calculate the external force required to hold the orifice in place. Neglect friction on the pipe wall.

Answer 1

Answer:

$=- 1.969*10^3lbf$

Explanation:

Given that:

Gage pressure at the inlet $P_{gl}$ = 20psig

Inlet diameter D = 4 in

Exit diameter d = 1.5 in

Volumetric flow rate at inlet

$Q_1$ = 2ft³?s

Applying continuity and the x component of the momentum;

we have:

Q = $V_1A_1$

$V_1A_1$ = $V_2A_2$

$V_1=\frac{Q}{A_1}$

$A_1= \pi \frac{D_1^2}{4}$

$A_2= \pi \frac{D_2^2}{4}$

Velocity at inlet is calculate as :

$V_1= \frac{4*Q}{ \pi D_1^2}$

$V_1= (\frac{4*2}{\pi *4^2})(\frac{144}{1} )$

= 22.92 ft/s

Velocity at the exit:

$V_2= \frac{4*Q}{ \pi D_2^2}$

$V_2= (\frac{4*2}{\pi *1.5^2})(\frac{144}{1} )$

= 162.98 ft/s

The required external force can be calculated by using the formula:

$R_x+P_{gl}A_l + \rho Q(V_2-V_1)$

$R_x=- P_{gl}A_l + \rho Q(V_2-V_1)$

$R_x=- (200)(\pi \frac{4^2}{4})+(1.94)(2)(162.98-22.92)$

$R_x=- 1969.84$

$R_x=- 1.969*10^3lbf$

Thus, the external force required to hold the orifice in place$=- 1.969*10^3lbf$