Can some one please explain what exactly is pressure ??? From thermodynamics point of view, it is clear. But how can we define pressure from Hydrodynamics point of view and we have learnt that as velocity increases pressure decreases according to Bernoulli's principle ( for straight stream lined flow). What is this pressure ?? It's also clear to me that Pressure is a scalar (it remains same irrespective of angle of orientation of point area on which it's acting) and different from normal stress whis is a tensor. It may sound silly querry however, i would like to convince me. Hoping constructive reply. Regards, Murthy

according to bernoullis principle pressure is teh driving force and as velocity increases pressure decreases, means that pressure energy is converted in kinetic energy.

and there was I thinking it was force per unit area

mechanical pressure is defined as negative of average normal-stress component(negative is taken since fluids can primarily support tensile stresses)

-p_bar = (sigma_11 + sigma_22 + sigma_33)/3

= -p + (lambda + 2*mu/3)*div(u)

where p is the thermodynamic pressure obtained from equation of state(perfect gas or van der Waals etc). If Stokes relation is satisfied (lambda + 2*mu/3 =0) then mechanical pressure and thermodynamic pressure are the same. Mechanical pressure is a measure of translational energy of the molecules only whereas thermodynamic pressure accounts for translational, vibrational and rotational (and for liquids other forms such as intermolecular attraction are to be included). Note that div(u) which represents the sum of the diagonal terms of the deformation-rate tensor is invariant w.r.t. a coordinate rotation(which is a similarity transformation). Cauchy showed that a unique definition of stress tensor can result only if stress at a point is defined at the intersection of any three mutually perpendicular planes (where the concept of F/A as the area shrinks to zero is employed).

That should read as fluids can primarily support compressive stresses

Thanq, Though I quite agree with upwind description, but somehow i couldn't convince me about pressure.It's clear that pressure is symmtric part of all normal stresses therefore it's a scalar.Can you please make me understand it. Thanks Upwind, Murthy

I think the best way to think of it is like voltage;

A pressure gradient in place causes fluid to flow, just as a voltage difference causes electrons to flow. Fluid system "Components" cause a pressure drop as you go through the system. Bigger pressure gradients gives more overall flow. A pump is basically a voltage source..also in a fluid system you generally fix the endpoint pressures and solve for what the flow will be in the system not the other way around.

Causes of pressure drops: -Friction in pipe -Height differences -Area gradients (and hence velocity gradients)

Causes of pressure rises: -Pumps, etc

Thanks David for your response.

It's clear that pressure gradient that causes flow and it's symmetric part of Sum of all Normal stresses but we are missing some thing when we define it some how.

Regards

Static Pressure can be thought of a collision of molecules on a surface placed in fluid.In a flowing fluid this surface is assumed to be kept parallel to axis of flow.When molecules collide on arbitrary surface , they exert a force.This foce exerted per unit area is known to us as pressure. I Think u have got the point.

Thanks a lot...yeah i got it now..How can we explain increase in pressure when there is a reduction in pressure...For this Do we need take into consideraton of translationl, vibrational n rotational motions??? I don't know exactly..Could you comment On it???

Sorry..Increase in pressure when there is reduction in velocity

Yes we can explain.You should think of pressure as normal force exerted on surface which is parallel to flow. when velocity is increased in a pipe, the force exerted by the fluid on pipe walls is decreased and hence static pressure is decreased.