Need MORE Hmwk help . Fluid mechanics, Fluids in motion, pressure

[LBRRIT2390]

College Physics

Homework Statement

The figure shows a section of a long tube that narrows near its open end to a diameter of 1.0mm. Water at 20celsius flows out of the open end at 0.020 L/s

What is the gauge pressure at point P, where the diameter is 4.0mm?

http://session.masteringphysics.com/problemAsset/1014234/7/jfk.Figure.P13.62.jpg

Homework Equations

Bernoulli's equation

The Attempt at a Solution

Same as my last post, no solution found yet. Please help me start and work through this problem.

 

[denverdoc]

Bernoullis here is quite simple and the basis for a venturi tube. In the initial frame you have lower kinetic energy and some potential energy from pressure, P. Some of that potential energy is traded for kinetic energy;

P1+1/2 rho(v^2)= P2 + 1/2 rho(v'^2). V' is the final velocity. From continuity of flow, the two velocities can be expressed as a ratio. That help?

 

[LBRRIT2390]

Thank you so much for replying!
So I plugged in everything that I calculated so far and ended up with:
P1 = P2 +49805

I can't figure out how to find the pressure in the smaller diameter tube so I can plug that in. I know it should be easy...I have the flow rate and the diameter, but I'm stuck.

Variables I've used:
rho=1000kg/m^3
Velocity1 = 0.623 m/s
Area of Larger section: 0.0126m
Velocity2= 10m/s
Area of Smaller section: 0.00785m

 

[denverdoc]

So you need a numerical answer not expressed in terms of p?

Edit: I reread the question it is asking for gauge pressure.

 

[LBRRIT2390]

Correct, a numerical value in Pascals. I think I need to incorporate the length of each section as well, not sure how though.

 

[denverdoc]

Well gauge pressure is relative to P. No length doesn't enter it unless you have frictional losses and data to compute these. More info would be given if it were needed.

 

[LBRRIT2390]

What do you mean by gauge pressure is relative to P?

Do you think that I am on the right track with the progress I've made? P1=P2+49806

 

[denverdoc]

What do you mean by gauge pressure is relative to P?

Do you think that I am on the right track with the progress I've made? P1=P2+49806

google gauge pressure. And yes.

 

[LBRRIT2390]

I was not able to get the answer before my assignment was due, the answer was 8.2E5 Pa.

But thank you, I really appreciate your help.