Question

In applying bernoulli’s equation, derive an equation for the pressure at the inlet of the nozzle below to produce a flowrate of Q=0.70ft^3/s. If the nozzle doscharges to atmosphere at point 2. Take diameters D1=3’’ and D2=1’’

Answer 1

Solution:

Given,

Flowrate of Q=0.70ft³/s = 1209.6 in³/s.

Diameters D₁=3 in and

D₂=1 in.

At section 1,

A₁ = = = 7.069 in²

P₁ = ?

At section 2,

A₂ = = = 0.7854 in²

P₂ =  The nozzle discharges to atmosphere at point 2 = 0

And

z₁ = z₂

Now,

Q = A₁V₁ = A₂V₂

V₁ = = = 171.11 in/s

And

V₂ = = = 1540.11 in/s

Applying bernoulli’s equation at sections 1 and 2, we get

=

Assume density of water = 0.03612729 lb/in³

And gravity g = 386.220472 in/s²

=

   

   = 1171330.09

  P₁ = 1171330.09*0.03612729

  P₁ = 42316.98 lb/in²