Pressure loss through a 90 degree bend

Hi so I've basically got some work to do where I have to calculate the pressure loss of a flow through 90 degree bends...however I've been searching and searching and have not managed to find a definitive equation for this. I've found many sources stating it is some form of coefficient involved, however in order to find the value of this coefficient the bend radius is required, which we were not told. If any one could help me that would be great...I'm kind stuck.

Often approximate values are given in literature; do you have a copy of Perry's lying around?

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Hey I've just come across another query and was wondering if you could help as you seem to know about this. I'm basically doing a lab report and have measured the pressure losses occurring through different pipe fittings etc. This included measuring the pressure loss across an entire venturi meter and and to the throat of the venturi meter. Now, from my results I'm seeing that the pressure loss across the entire pipe is less than the pressure loss to just the throat of the venturi meter...is there any chance you can explain why this is? Cheers

If I understand you correctly, you are measuring from the entrance to the Venturi meter to the exit of the Venturi meter, and from the entrance to the throat. You are wondering why the first case has a lower pressure drop than the second case. Is that correct?

Anyway, I will answer your question as I understand it.

The pressure drops at the throat, because if we are assuming steady state operation, then as the pipe narrows the fluid must have to increase in velocity to compensate for the lower cross-sectional area to flow through. Note that due to conservation of mass, $\rho_1 v_1 A_1 = \rho_2 v_2 A_2$. For an incompressible fluid (usually assumed) the density will remain constant and $A_2$ is smaller, so $v_2$ has to increase to maintain the same mass flowrate through the pipe.

If you look at the Bernoulli equation, if no change in elevation occurs, then the only relevant things to consider are the kinetic energy (velocity) term and the pressure term (and frictional losses). As the velocity increases, the pressure will have to decrease (conservation of energy).

Lastly, the pressure difference between the entrance and exit of the Venturi meter will be smaller because the cross-sectional areas are the same, resulting in similar energies per unit mass, save the losses due to friction from the Venturi meter (contraction/expansion) and frictional losses from the pipe wall.

Hope this helps.

If I understand you correctly, you are measuring from the entrance to the Venturi meter to the exit of the Venturi meter, and from the entrance to the throat. You are wondering why the first case has a lower pressure drop than the second case. Is that correct?

Anyway, I will answer your question as I understand it.

The pressure drops at the throat, because if we are assuming steady state operation, then as the pipe narrows the fluid must have to increase in velocity to compensate for the lower cross-sectional area to flow through. Note that due to conservation of mass, $\rho_1 v_1 A_1 = \rho_2 v_2 A_2$. For an incompressible fluid (usually assumed) the density will remain constant and $A_2$ is smaller, so $v_2$ has to increase to maintain the same mass flowrate through the pipe.

If you look at the Bernoulli equation, if no change in elevation occurs, then the only relevant things to consider are the kinetic energy (velocity) term and the pressure term (and frictional losses). As the velocity increases, the pressure will have to decrease (conservation of energy).

Lastly, the pressure difference between the entrance and exit of the Venturi meter will be smaller because the cross-sectional areas are the same, resulting in similar energies per unit mass, save the losses due to friction from the Venturi meter (contraction/expansion) and frictional losses from the pipe wall.

Hope this helps.

Ok this is the last question I promise. Am I right in thinking the Reynolds number changes in the Venturi meter due to the changing pipe diameters?

Yes, $Re=\frac{Dvp}{\mu}$. The diameter and the velocity of the fluid will be different between the entry and throat, in turn affecting the Reynolds number.

I'd just like to add that be careful about talking about Reynolds number by changing the length dimension. I'm certainly not an expert, but I'd wager that it'd change because of velocity changes and you'd keep the length fixed based on some flow characteristic.

I don't follow.