Calculate Pressure in Fluid Motion Pipe with Bernoulli's Principle

[lazypast]

hi, I am just assumin this is the right place for bernoulli stuff

pressure 1 and 2 are both static pressures, and the arrow shows fluid motion

is it possible to calculate them directly from an equation? or is it simply P1 and P2?


and also, since the diameter decreases for P2, the kinetic energy will increase, and so the pressure energy decrease.
because of this, will static pressure (shown by P2) be smaller than P1 ?

thanks
(attacked photo shows my highly complex diagram)

 

[Andy Resnick]

It is possible to calculate the pressure difference directly, but you need to supply some addtional information, such as:

1) the inlet and oulet pressures
2) fluid viscosity and density
3) information about the neck region- does it perturb the flow, or does Poiseuille flow (approximately) hold in both sections?

 

[lazypast]

hm i should of told you, fluid viscosity neglected (or just ignored), and no friction losses occur.

 

[rcgldr]

The assumption in this case are:

Total energy is a constant = C = pressure energy + kinetic energy = pressure + 1/2 m V^2.

V changes inversely with cross sectional area of the pipe = pi x R^2.

Note that the equation, C = pressure + 1/2 m V^2 implies that if velocity is high enough, pressure would be negative, which can't happen in real life.

 

[swapnilster]

If you just want to find a relation between the two pressures, just use both -bernoulli's eqn and continuity eqn and assume a few quantities like r1>r2 .Also in bernoulli's eqn neglect gravitational potential energy.
1/2 d V1^2 +1/2 m V1^2=1/2 d V2^2 + 1/2 m V2^2
v=velocity
d= density
m= mass of water flowing per second thru unit cross-section->m1=d pi r1^2

 

[wwinquang2003]

Great, that master I also consider a long time, but I can't find myself the satisfy answer. Because
If we base on the bernoulli equation and principle. It is easy to see as above. But should attention in the condition to apply bernoulli. And other question is:
1. In piping system with liquid flow inside, what pressure we measure? call it is measurement pressure
2. Measurement pressure in the pipe 1 (large diameter) is higher than measurement pressure in pipe 2 or lower than?

Please consider!1

 

[russ_watters]

Given the simplifying assumptions discussed above, the difference between p1 and p2 is a matter of the area ratio and velocity only (as shown in Bernoulli's equation).

In real life, where viscosity plays a role and you have boundary layers, larger pipes will experience less static pressure loss through them than smaller pipes at the same velocity.