Water flow through a horizontal pipe

Question

 Water flows through a horizontal pipe. The nozzle inlet has a cross sectional area (Ain) of 240mm2; the nozzle outlet has a cross sectional area (Aout) of 80mm2.  The inlet velocity is 4 m/s. Calculate the mass flow rate (Q) the inlet pressure (Pin).  

Answer 1

The mass flow rate is rho*A1*v1

 

Assume water is incompressible, use conservation of mass to find the outlet velocity:  mdot1 = mdot2 or

 

A1*v1 = A2*v2

 

 

Now use Bernoulli's Equation to solve for the inlet pressure. Assume the outlet is at atmospheric pressure.

 

1/2*rho*v1^2 + rho*g*z1 + p1 = 1/2*rho*v2^2 +rho*g*z2 + p2

 

Solve for p1