# Fluid Mechanics: How does flowing fluid have pressure in it?

Basically, I know that fluid at rest have pressure. But how does a flowing fluid have pressure in it? Pressure is force per unit area. Flowing fluid have force in it but there is no cross-section area ti exert the force so how does flowing fluid have pressure in it?

• Imagine a bubble floating in the fluid. Think about the "thin skin" of the bubble. Is there pressure on that skin? Does it matter if the fluid is moving? Does it matter if the bubble even exists? – Mike Dunlavey Oct 7 '16 at 12:59
• If you move relative to a stationary fluid, which you've admitted that has some pressure in it, then you'll see a flowing fluid! – SaMaSo Oct 7 '16 at 13:11

## 3 Answers

You don't need to have a solid surface for pressure to exert a force. Pressure exerts a force at the conceptual boundary between all fluid parcels within the fluid, not just at solid surfaces.

Why would you think that there is no cross-section area on which the force is exerted? Imagine a tube with a constant radius full of water that is opened on both ends. Let's say that the cross-section of this tube has an area $A$. Since the tube has a constant radius, wherever you choose to cut the tube, the area of the cross-section will be $A$. Now let's say that you apply a pressure of $100~Pa$ on one end of the tube and a pressure of $50~Pa$ on the other end. Will the fluid flow?

Well, the fluid will flow only if there is some acceleration, and that happens only if $\sum F\neq 0$ (Newton's Law). Well let's look at the pressures. $$P_1=100 ~Pa \Rightarrow P_1=\frac{F_1}{A}$$ also $$P_2=50~Pa\Rightarrow P_2=\frac{F_2}{A}$$

Since $P_1>P_2$ and since $A=const.$ we conclude that $F_1>F_2$ thus it is true that $\sum F\neq0$ and therefore $a\neq0$ and from all of this we conclude that the fluid is moving! So not only there is pressure inside of the flowing fluid, but also without a difference in pressures the fluid wouldn't move at all!

• I got your point. I am not saying there is no area but I am saying that area does not have any surface or boundary. In static pressure there is physical surface where force is exerted and hence pressure is created but in fluid flowing there is no surface where force is exerted and pressure is created unless you say that flowing fluid have layers and one layer layer exerts force on another and hence chain reaction. This is my theory. Is this right? – Obaid Ur Raza Muhammad Rafique Oct 7 '16 at 14:01
• A fluid that is in laminar flow does have physical surfaces upon which a force can be created. And I don't really understand your "area does not have any surface or boundary", you do realize that area is a physical quantity with which we describe surfaces that have boundaries? Also, every fluid that is in laminar flow can be described as bunch of layers flowing on top of each other and it is true that there is somewhat of a "chain reaction" causing any difference in pressure to spread out through the whole fluid. Read (en.wikipedia.org/wiki/Pascal%27s_law) – bonehead Oct 7 '16 at 14:09
• @ObaidUrRazaMuhammadRafique You don't need to have a solid surface for pressure to exert a force. Pressure exerts a force at the conceptual boundary between all fluid parcels within the fluid, not just at solid surfaces. – Chet Miller Oct 7 '16 at 19:52
• @ChesterMiller I think that should be an answer :) – Sanya Oct 7 '16 at 21:07

Almost all of the fluid has a surface to exert pressure, in either laminar or turbulent flow. The fluid itself. The back of the fluid relative to flow has more potential for pressure than the front. Pretty much what Chester Miller is saying.

• Can you explain me why front of the flow have less pressure than the back of the flow. – Obaid Ur Raza Muhammad Rafique Oct 8 '16 at 11:47
• I'm assuming the fluid is flowing through air or something like it and a pump started the flow. There would be more mass near the back of the fluid even with what we call a non compressible liquid than the very front especially the interface at the front between the flow and the air verses the rear. The flow is not pulled in this instance but rather pushed, kind of like when pushing a piece of Play-dough. The rear folds before the front because it experiences more pressure. – william deets Oct 11 '16 at 23:57