Question

Water at 68 deg F flows in a 6 inch diameter smooth pipe. What flowrate in gallons per minute is flowing if the pressure drop across a 3 in diameter long radius nozzle is .525 psi? What is the Cd (Coefficient of Discharge)? GPM>?

Answer 1

Given,

Dia. of pipe, (D) = 6 in.

A₁ = D² = *6² = 28.27 in²

Dia. of Nozzle, (d) = 3 in.

A₂ = d² = *3² = 7.068 in²

Pressure drop (p₁ - p₂) = 0.525 psi

From continuity equation,

A₁V₁ = A₂V₂

28.27V₁ = 7.068V₂

V₁ = 0.25V₂

Now,

Applying Bernoulli's equation at sections 1 & 2, we get

+ + z₁ = + + z₂

But,

z₁ = z₂

   + = +

-   =   -

   =  

     =  

0.03768 = 1.209*10^-3*

= 31.16

V₂ = 5.583 in/s

Theoretical discharge (Q) = V₂*A₂ = 5.583*7.068

Q = 39.46 in³/s

Q = 10.249 gallons per minute

Assume ,

Actual discharge (Q_act) = V₁*A₁

But,

We know,

V₁ = 0.25*V₂ = 0.25*5.583 = 1.395 in/s

(Q_act) = 1.395*28.27 = 39.44 in³/s

(Q_act) = 10.243 gallons per minute.

Now,

C_d = Coefficient of discharge

We have,

C_d =

C_d = = 0.99