Fluid Mechanics Help: Questions Answered

[Urmi Roy]

fluid mechanics...

Hi,everyone.
I'm doing the second of my mechanical engineering course and I've been doing fluid mechanics lately...I have some questions...could some ony please help me with them?

1.In Bernoulli's theorem,it basically states the if we have an ideal liquid (Newtonian) undergoing steady flow,wherever the velocity increases,the pressure of the liquid decreases. Now,intuitively,does this mean "When the liquid starts flowing fast,it doesn't have the time to impose a pressure on the walls of the pipe because it's rapidly flowing away?"

2.in an inverted differential manometer,how do we find the pressure equation for equilibrium conditions of the maometer liquid?(I mean the net upward pressures on the manometric liquid is it's own weight,isn't it?)

3.Generally,why do we use all these different kinds of manometers...inverted differential manometer,upright differential manometer,etc.?Do they have any individual/specific functions?

4.We often use thermodynamic equations (like the steady flow Energy Equation) for even water and other liquids...but is this permissible?...because in liquids,we have to account for inter-molecular atraction,and cannot treat it as an ideal gas(which we always assume in thermodynamics).

 

[Studiot]

I know you have been studying thermodynamics recently.

1) Bernoulli's theorem like the First Law is just another presentation the law of conservation of energy. If a fixed parcel of fluid (= a control volume) is moving faster, then since it has constant total energy it's potential energy (pressure) must drop to compensate for its increase in kinetic energy.
Time does not enter into it.

2)In a differential manometer, inverted or not, you have a tube of liquid with different pressures pushing in opposite directions across the ends of the fluid in each leg. This causes a difference in the positions (levels) of the fluid surfaces in the legs. The product of the difference in pressure times the tube (liquid) cross sectional area equals the weight of the manometer fluid displaced = manometer fluid density times the difference in level times the cross sectional area. So you can see the area of the tube cancels out.

3)Convenience at specific locations.

4)Thermodynamics applies to all substances, not just ideal gasses. Some theory is obviously not appropriate for some substances. The intermolecular forces affect the internal energy of the substance.

 

[Urmi Roy]

Time does not enter into it.

No,actually I didn't exactly mean time...it's more that the fluid doesn't bother to exert pressure anymore when it has greater velocity.(just trying to find a way to explain it to myself!)

2)In a differential manometer, inverted or not, you have a tube of liquid with different ...So you can see the area of the tube cancels out.

Suppose the pressure in the pipe is Pa on one side,the net pressure in that leg of the manometer is Pa-(rho of pipe liquid in that leg)xgxheight ...similarly,on the other side,it's Pb-(rho of pipe liquid in that leg)xgxheight ...
Each of these is the net pressure of the pipe liquid on the manometric liquid...why do we use the minus sign in each of the expressions(in upright manometer,it's Pa+(rho of pipe liquid in that leg)xgxheight )...secondly,isn't the Pa-(rho of pipe liquid in that leg)xgxheight the weight of the manometric liquid in the respective column?

 

[Studiot]

isn't the Pa-(rho of pipe liquid in that leg)xgxheight the weight of the manometric liquid in the respective column?

The fluid flowing in the pipe may not even be a liquid!

The weight of anything = volume times density.

It is the manometric liquid that is displaced by the pressure difference, so it is the weight of this displaced manometric liquid that we consider.

Draw a diagram and convince yourself.

 

[Urmi Roy]

Okay,so why is it Pa-(rho of pipe liquid in that leg)xgxheight ?

 

[abhishekkgp]

bernoulli's eqn does not state that wherever the velocity of fluid increases,the pressure of the fluid decreases. there is a gravity head too... so even if velocity increases in some direction then the pressure gradient may still be positive in that direction.