Error in the Hooper method for conical diffuser/expansion

[AllanBjerg]

Dear Caleb,

It is a great tool that you have developed!

I am currently working with the Hooper method for a conical diffuser/expansion from the fluids.fittings library. I think there is a small error for the case of Re_1 < 4000 and angle < 45°. It returns K = K_sharp while it should return K = K_sharp2.6sin(angle/2).

Code is stated below:
elif method == 'Hooper':
if Re is None:
raise ValueError("Method Hooper requires Reynolds number")
if Re < 4000.0:
return 2.0*(1.0 - betabetabetabeta) # Not the same formula as Rennels
if fd is None:
fd = Clamond(Re=Re, eD=roughness/Di1)
x = 1.0 - betabeta
K = (1.0 + 0.8fd)xx
if angle_rad > 0.25pi:
return K
return K2.6sin(0.5*angle_rad)

Best regards,
Allan

[Caleb Bell]

Hi Allan,
I took a quick look and here is the original formula from the paper:

These look to me to be the formulas I've implemented.
Can you clarify what you are asking? I don't understand.

[AllanBjerg]

Hi Caleb,

I agree that these formulas are implemented correct but I am talking about the diffuser and not the reduction.

When I run the code for an expansion the result for K for a conical expansion at Re < 4000 and angle < 45° is the same as for a sharp expansion. As per the Hooper paper for these conditions the expression for K should be multiplied by: 2.6 x sin(angle/2). I don't think this happens in the code. See example of calculation below:

Since we are in the range Re < 4000 and angle < 45° for the conical expansion, the K value should not be the same as for the sharp expansion. If the value is multiplied with 2.6 x sin(angle/2) the resulting K = 1.2617.

I hope that this clarifies my question.

Best regards,
Allan