Question

A horizontal pipe is fitted with a nozzle. The inlet diameter of the nozzle is 40 mm and the outlet diameter is 20 mm. The flow rate in the pipe is 1.2 m3 /min and water density is 1000 kg/m3 . Determine the force exerted by the nozzle on the water.

Answer 1

969.68N

Step-by-step explanation:

d₁=0.04 m A₁=
`(\pi d^2_(1)  )/(4)`

`A_(1) =(\pi * .04^2)/(4)= 0.00125m^(2) \`

d₂=0.02 m A₂=
`(\pi d^2_(2)  )/(4)`

`A_(2) =(\pi * .02^2)/(4)= 0.00031m^(2) \`

Q=1.2m³/min Q=1.2/60=0.02m³/s

using continuity equation

Q₁=A₁v₁

v₁=Q₁/A₁=0.02/0.00125=16m/s

Q₂=A₂v₂

v₂=Q₂/A₂=0.02/0.00031=64.5m/s

`F_(inlet)=\rho A_(1)v_1^(2)`

`F_(inlet)=1000* 0.00125*16^(2)=320N`

`F_(outlet)=\rho A_(2)v_2^(2)`

`F_(outlet)=1000* 0.00031*64.5^(2)=1289.68N`

Force on the nozzle=F_{outlet}-F_{inlet}

= 1289.68-320

=969.68N