Fluid Velocity and flow rate questions

[Creaton1]

I am going over a past paper and this is my last question I am stuck on. Once I can solve this I can finally progress. This is from a past paper and my exam will be on a variation of the question.

Can someone please talk me through the questions, displaying the method, calculations and equations needed to answer each part.

http://postimage.org/image/33j1ag9fo/ - Question and Diagram.

I have to determine:

- Velocity of petrol through the pipe
- Mass Flow of petrol
- Manometer reading if the flow rate were reduced by 50%

I know v1*p1 = v2*p2 = const,

Regards,

Will

 

[edgepflow]

You will need to use the Bernoulli equation in conjunction with the continuity equation to find the ideal flow. Then use the value and definition of discharge coefficient to find the real flow.

 

[Creaton1]

How do I figure out velocity? p1 - p2? how do i work that out?

 

[edgepflow]

OK, I will give you some hints.

First, write the Bernoulli Equation:

P1 + p v1^2 / 2 = P2 + p v2^2 / 2

And you are trying to find v1, the velocity in the pipe. Then use the continuity equation v1* A1 = v2 * A2 and solve for v2 = v1 * A1 / A2.

Plug this expression for v2 into the Bernoulli equation and solve for v1. Everything is given to do this !

Work on it - let me know if you need any help. This is one of the most basic and practical fluid dynamics solutions there is.

P.S.

You can figure P1 - P2 from the difference in column levels in the manometer (called the manometer "deflection").

 

[W R-P]

Hi I just registered on this site, I recently received my BSc in Mechanical engineering so I thought I'd take a quick try at it, sorry about the handwriting-bare with me. ANYONE PLEASE CORRECT ME IF I'VE GONE WRONG SOMEWHERE.
http://postimage.org/image/8fq8490-
for the last part c), the initial value of the flow rate from b) is halved.This means the velocities will also change. Find V1 using Q(m3/s) or m (kg/s), then work backwards from V1= 2gh/((m^2)-1) to find h in terms of petrol. You can also find h in terms of mercury (depending on what the examiner wants) using the density relation I applied(it's actually a pressure relation,but the Rho's on both sides cancel out) .
I hope this helps,
William