Pressure drop across a thick orifice

[nlis12]

Greetings,

I am trying to understand how to setup/solve for the pressure drop across an orifice L=3.5in

The pipe diameter starts at 1in, then abruptly decreases to 0.5in for the length of the orifice, and abruptly transitions to 1in diameter. (See the attached file for an illustration.)

Assuming I know the flow rate of the water, how can I solve for the pressure drop across this orifice?

Any information is appreciated!
Thanks!

 

[jrmichler]

Start by applying the results of your earlier post: https://www.physicsforums.com/threads/pressure-drop-across-a-change-in-diameter.942158/. Show your calculations, add some dimensions, then ask again. Note that the dimensions (more correctly ratios) do make a difference in this particular case.

 

[Chestermiller]

How accurate does the answer have to be? What is the water flow rate?

 

[nlis12]

Start by applying the results of your earlier post: https://www.physicsforums.com/threads/pressure-drop-across-a-change-in-diameter.942158/. Show your calculations, add some dimensions, then ask again. Note that the dimensions (more correctly ratios) do make a difference in this particular case.

Here is my work. I assumed 3 regions. 1=before the orifice 2=in the orifice 3=after the orifice.
The fluid is water.
I broke the problem up into 2 parts.
Part 1: Transition between region 1 and 2
Part 2: Transition between 2 and 3.

I chose diameter of 1in in regions 1 and 3 and a diameter of 0.5in in region 2...
I also chose an input flow rate of 2gal/min in region 1.

I calculated a pressure drop of 0.044psi for both of the halfs of the problem. Totaling 0.088psi across the orifice. (does this seem correct?)
Also, how can I account for the length of the orifice in my problem?

Thanks!

 

[nlis12]

How accurate does the answer have to be? What is the water flow rate?

You get to choose the flow rate/velocity and the dimensions of the problem are set for you.
I chose 2gal/min as a nominal value.
I'd like to solve the problem as accurately and precisely as possible.

Thanks!

 

[Chestermiller]

Bird, Stewart, and Lightfoot, Transport Phenomena, give the friction losses for different types of changes in cross sectional area in the form:
$$\Delta p=\frac{1}{2}\rho v^2 e_v$$where v is the downstream velocity and $e_v$ the "friction loss factor." For a sudden contraction, they recommend $$e_v=0.45(1-\beta)$$and, for a sudden expansion, $$e_v=\left(\frac{1}{\beta}-1\right)^2$$where $\beta$ is the smaller cross sectional area divided by the larger cross sectional area.

In the straight section, the L/D is 7, so the flow should not be fully developed. Still, for a lower bound, I would use the pressure drop for fully developed flow in a pipe of this diameter, and for an upper bound, I would use the pressure drop equivalent to the shear force at the wall in the hydrodynamic entrance region (i.e., essentially flow over a flat plate with the same free stream velocity as the mean flow velocity).