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?
 A: 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. 
A: 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!
A: 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.
