Mechanical engineers!

[Howard]

Need some help with this problem.

Imagine I have a vertical tank, conical bottom, with a bottom discharge. The bottom discharge has a pipe tee connected such that the tee is pointing horizontally. The tee connection has a PI (pressure gauge) which, under zero flow, shows a non-zero gauge reading due to hydrostatic pressure. Tank could be full of water, whatever.

When the two bottom outlets shown in the picture start delivering a flow, there will be a velocity > 0 in the pipe tee. What equation do I use to calculate the difference in gauge pressure based on fluid velocity?

I'm not too certain Bernoulli's principle necessarily applies here - unless I just use conservation of energy?

 

[Howard]

Equation 15-14 here?

http://courses.ncssm.edu/apb10/resources/guides/G15-1.bernoulli.htm

EDIT: Damn it, my dimensional analysis is failing. I have v1 = 0 (no flow) and I've set P1 = 0 as I am looking only for pressure difference. The 1/2(rho)(v2)^2 term is giving me units of kg/(m*s^2) whereas force requires kg*m/s^2... what is going on?

rho is kg/m^3, squaring the velocity term can only give me m^2/s^2, the last m stays on the denominator but I need it on the numerator to get Newtons

 

[PieIsAwesome]

I am not too sure as I haven't taken this stuff in a while, and I'm not sure what the point of having a tee there instead of a valve with a single outlet is for whatever this problem is trying to teach, but:

Maybe Bernoulli equation with one pt. set at the tank and another at the tee.

P1 = tank pressure
V1 = 0
z1 = tank height
P2 = pressure at gauge
V2 = average fluid velocity at gauge
z2 = gauge height or 0 if this is your datum.

EDIT: It seems point 1 has already been chosen for you as somewhere below the tank, so V1 is not zero there.
P1 = given pressure at pt. 1
V1 = speed at pt.1
z1= height at pt. 1

 

[Puppies04]

42

 

[Howard]

I am not too sure as I haven't taken this stuff in a while, and I'm not sure what the point of having a tee there instead of a valve with a single outlet is for whatever this problem is trying to teach, but:

Maybe Bernoulli equation with one pt. set at the tank and another at the tee.

P1 = tank pressure
V1 = 0
z1 = tank height
P2 = pressure at gauge
V2 = average fluid velocity at gauge
z2 = gauge height or 0 if this is your datum.

EDIT: It seems point 1 has already been chosen for you as somewhere below the tank, so V1 is not zero there.
P1 = given pressure at pt. 1
V1 = speed at pt.1
z1= height at pt. 1

I'm not concerned about heights at this point. What I need to do (and this is a practical problem, not an academic one) is determine whether or not I can put the PI where the tee is.

Basically, I am using hydrostatic pressure to measure the level of the tank. When all flows are zero, it works very effectively as shown. However, as flow across the PI increases, I believe the pressure will begin to drop due to the increased velocity. As the pressure drops, the PI reading becomes less and less accurate. For example, if the liquid level of the tank is maintained through some external means, and the output flow goes faster and faster, I could expect to see the PI reading drop more and more, even though I want it to be steady (showing the exact liquid level).

You can use my fluid velocity for calculation - it is 2.83 L/s. Pipe diameter at the region of the PI is 100 mm (ID).

 

[Howard]

So anyway, as above, I have an equation P1-P2 = 0.5 * ... whatever

But the units don't make sense to me. I am doing something fundamentally wrong, I think, as the term on the right hand side is not a pressure. Force (N) is kgm/s^2, whereas pressure is (kgm/s^2)/m^2... OK, I got it now.

 

[Howard]

With pipe ID 97.4 mm, velocity of 0.38 m/s, the pressure drop is 72.3 Pascals or 0.01 psi. This equates to a change in level reading of 7 mm (assuming rho = 1000 kg/m^3), which is negligible, therefore I can use a PI to measure tank level.

 

[PieIsAwesome]

I'm not concerned about heights at this point. What I need to do (and this is a practical problem, not an academic one) is determine whether or not I can put the PI where the tee is.

Basically, I am using hydrostatic pressure to measure the level of the tank. When all flows are zero, it works very effectively as shown. However, as flow across the PI increases, I believe the pressure will begin to drop due to the increased velocity. As the pressure drops, the PI reading becomes less and less accurate. For example, if the liquid level of the tank is maintained through some external means, and the output flow goes faster and faster, I could expect to see the PI reading drop more and more, even though I want it to be steady (showing the exact liquid level).

You can use my fluid velocity for calculation - it is 2.83 L/s. Pipe diameter at the region of the PI is 100 mm (ID).

I don't know how you can ignore the height.

If we set pt.1 to be at the top of the fluid within the tank, and pt.2 to be at the gauge, then:

P2 - P1 = 0.5 (rho) (v1^2 - v2^2) + (rho) (g) (z1 - z2)

What this shows is that there the pressure difference is the result of a velocity difference and a height difference.

When the flow is zero, the velocity term in the above equation is gone, so you are just left with the hydrorstatic pressure due to fluid height.

When there is fluid flow, you need to take into account the velocity term.

 

[PieIsAwesome]

Oh, I see, you were trying to see how much of an effect the velocity had on the pressure difference, and if its small enough to ignore it.

 

[Imp]

Bernoulli?

 

[Howard]

Oh, I see, you were trying to see how much of an effect the velocity had on the pressure difference, and if its small enough to ignore it.

Yes, exactly.

 

[alkemyst]

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[dank69]

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[alkemyst]

Slow your roll.

 

[darkewaffle]

I think it's for a doublenema.