I'm not sure if I got your point, but may be you are confusing stationary flow with fluid at rest? The static pressure is the result of both the external forces from the BCs and the fluid body force.

If I understood your question correct.

In fluid which flow along a pipe with radius r, the total pressure

Ptot=Pstatic + Pdynamic

Actually, the origin of this equation is the energy conservation law. The work done on the fluid from the total pressure is equal to the kinetic energy of the fluid, which moves, plus the potential energy of the fluid at rest due to its position in the gravitational field. If you follow derivation (from any fluid mechanics book), Pstatic is the Potential energy U/Volume=mgh/V=rho g h,

And Pdynamic=(1/2) rho v^2. g is gravitational acceleration, h is the distance of the axis of the pipe from the ground (taken as distance zero from surface of earth).

@ C. Martin Saravia.

Yes I suppose this could have been a much better way of putting this question. Kindly correct me if I am wrong in interpreting and posing my question correctly.

Fluid at rest has a body force (due to its weight) while in case of fluid flow the forces may be due to shear for due to inertia of fluid and all those acting on it account for static pressure.

Kindly correct e here if its correct to say that force due to change in momentum of fluid which accounts for its acceleration (just like in solids) contributes to static pressure while its velocity provides it kinetic energy which forms part of dynamic pressure.

Thanks

Static pressure is the actual pressure of the fluid ( which you can actually measure) and IT IS NOT associated with its motion but with its state.It is what we normally call just Pressure.Now, in many fluid flows changes in elevation are insignificant and may be ignored.We then have Bernoulli's equation

P+0.5ρV**2=Ptotal. static+dynamic=total.The total is constant along any streamline(for irrotational flow everywhere).

Every point in a moving fluid has its own static,dynamic and total pressure.

@ Deewakar Sharma. Not true. As N.C Markatos says, static pressure is not associated to fluid motion (neither acceleration nor velocity). Static pressure has 2 components: a) Fluid body force b) Static pressure distribution in the pipe as a result of the static pressure difference between inlet and outlet. The second is what causes the fluid motion (if the pipe is horizontal)

I Can refer a book which can help you out for your question The Book’s name is “Fluid Mechanics “ by Yunus A.Cengel and John M. Cimbala

The terms STATIC PRESSURE and HYDROSTATIC PRESSURE/HEAD are your problem.I would suggest you dig into basics once more.

From an experimental view point :

To contrast the concept of static pressure and hydrostatic pressure (P=rho*g*H), i will suggest you the following steps.

(1) Choose an axial section on the pipe, where you want to measure the static pressure. (2) Now Make a small hole on the pipe at that axial location (3) Insert a small tube (SS tube) perfectly fitting without any leakage This is called a pressure tap (4) Now , connect this pressure tap to an open-to-atmosphere water/liquid manometer. Then the liquid (density 'rho') column rises to a certain height 'H". The P=rho*g*H we are talking about is the hydrostatic pressure. The Static pressure of the fluid inside the pipe is only being measured through an indirect means. Static pressure measured from the liquid manometer is P_atmospheric + (rho*g*H).

Now question yourself ?? (If gas were to flow in the pipe what would be the case?)

But your version of pressure i.e. Hydrostatic pressure w.r.t. the pipe dia, within the pipe is not considered (neglected), and it holds good for very very dense liquids flowing through very very big (large dia) pipes.

assume a large tank of water and the height of the water is 10 m. a pipe of 10 cm is connected to its side. The total head = 10 m= static pressure + dynamic pressure + height (at any section on the pipe).

consider the pipe is keep at same diameter for long distance. the total head will be split into dynamic head (velocity) and static head. if the diameter is constant, then the dynamic head will be constant.

The difference between the total head and the dynamic head will be static head.

if the pipe diameter decrease, part of the static pressure will transferred to velocity (dynamic head) and static pressure decreased.

It is not important if it is a pipe flow or any other kind of flow.

The static pressure is the one that is measured by a gage that has the same local velocity of the flow i.e. that it is stationary with respect to the fluid.

To measure it in a pipe flow, as long as if you have a sufficient straight lenght upstream and downstream (about ten pipe diameters upstream and five downstream) of the measuring section, you can drill four small holes in the pipe wall, put an annular chamber around them and measure the pressure of that chamber. Pay attention not to have burrs at the holes exit in the internal pipe wall, that may cause dynamic effects.

I have a similar doubt related to this concept of fluid flow in pipe'

Situation -

In a pipe 20 mtr long a pressure gauge (P2) is installed 0.5 mtr before outlet and at other end fluid is pumped in pipe at certain intial pressure P1.A flowmeter is installed in line just before P2.

Case : - 1

P1 = any value , P2 = 2 kg/cm2 and flow through pipe = 100 l/hr.

Case:-2

P1 = anythig , P2= 5 kg/cm2 and flow through pipe = 100 l/hr

My doubt is

1. is it practically possible to have case 1 and case 2.

2.if yes, then how can i look and differentiate by my eyes between 100 ltr/hr flow at 2kg/cm2 and 100ltr/hr flow at 5kg/cm2.

Practical application of this

1.We have a granulating pan which revolves powder inside it and water is sprayed at 1lit/min by a 1/2" line (at mouth a nozzle is connected to produce spray).Water is pumped by reciprocating pump.

2.My task is to replace this pump by centrifugal pump.Install a automatic valve in 1/2" line to get required flow rate and pour back extra pumped water to tank by re circulation line.

3.They asked our requirement is 1lit/min flow at 3.4kg/cm2 because then only spray would form.

4.My doubt is that spray is due to velocity change. in pipe Q = A1V2 and through nozzle Q=A2V2 since nozzle has small A2 hence V2 is high so water comes out at higher velocity and go more in form of spary.

So you require 1lit/hr flow through that 1/2" pipe.What is significance of saying 3kg/cm2 pressure.

But some how i know this is the way we talk in industry.I need x flow at Y pressure Similar to like a electrical equipment say i need 1 amp at 230V.

please help me to understand this or at least guide me for its understanding.