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ram June 15, 2000 11:49

fluid flow fundas
 
hi.. i am having some doubts in fluid flow.. 1. what is the difference between darcys friction factor and fannings friction factor? why do we need 2 friction factors to define? 2.this is an example..as u know if a pipe is put inside a flow field, we obtain parabolic profile for velocity..lets say flow takes from left to right..the pipe ends are end A at the left and end B at the right..now we all know that pressure drop takes place across the flow inside the pipe..it implies that the pressure at end B is less than the pressure at end A.. does it imply that the flow shall take place from end B to end A as the pressure at B is less? in reality in a wind tunnel it doesnt happen..how can u explain this theoritically? 3. how can we say that flows are dynamically similar in 3D unsteady flow fields? can we use reynolds no.? if so how should it be defined?

thank u for ur kind attention regards ram

Raza Mirza June 15, 2000 12:26

Re: fluid flow fundas
 
"lets say flow takes from left to right..the pipe ends are end A at the left and end B at the right..now we all know that pressure drop takes place across the flow inside the pipe..it implies that the pressure at end B is less than the pressure at end A"

Correct.

"does it imply that the flow shall take place from end B to end A as the pressure at B is less? "

No it implies flow from A to B as flow takes place from higher to lower pressure. Analogy with electric current flow is often used where the current flows from higher to the lower potential.


Alton Reich, PE June 16, 2000 14:40

Re: fluid flow fundas
 
Ram,

By the numbers:

1. The Darcy friction factor is taken from the Moody diagram or a curve fit of it. It is a function of the Reynolds number and the relative roughness of the pipe.

The Fanning friction factor is a function of density, velocity and wall shear stress.

From a practical engineering standpoint, the Moody diagram (or a curve fit) is almost always used because it depends on things that you know. I know or can measure the pipe diameter, flow velocity, fluid density and viscosity. The relative roughness can be obtained from a handbook or from the pipe vendor. That's all I need to use the Moody diagram. On the other hand, I've never met an engineer in the field who could tell me the wall shear stress in any of his piping systems.

As an interesting aside, Darcy friction factor = 4 * Fanning friction factor

2. Picture a simple closed loop piping system. I've got a pump, and the piping from the outlet of the pump connects to a throttle valve. The piping from the other side of the valve connects back to the inlet side of the pump. Which way is the flow going? It goes from the outlet of the pump to the valve an back to the inlet of the pump. The pump adds energy to the system and there is a pressure rise across the pump. The fluid at the outlet of the pump is at a higher pressure than the fluid at the inlet. Because of the spinning impeller, the fluid can't go backwards through the pump, so the high pressure fluid travels down the pipe toward the valve. As it moves it looses energy due to frictional effects. After traveling around the system back to the inlet of the pump, the fluid is at low pressure again.

It comes down to this, in an open or closed piping system the fluid is driven entirely by pressure differential. In your example, flow goes from A to B because the pressure at A is greater than at B. If the pressure at B is raised, the flow rate would slowly decrease, and reverse when the pressure at B became greater than at A. (This is why check valves were invented.)

3. Here we have to be very careful what we're talking about. Many things do scale well with a constant Reynolds number. If I have a real object, like a ship, and I set up a scale model that operates at the same Reynolds number I can expect some non-dimensional quantities, like pressure coefficient, drag coefficient, and velocities, to match reasonably well. However, turbulence quantities do not scale nearly as well. The size and intensity of separated regions will not scale well at all. This is one of the reasons that in industries that used to rely heavily on scale model testing the move to enbrace CFD analysis has been very strong.

Hope this helps, Alton

John C. Chien June 16, 2000 20:41

Re: fluid flow fundas
 
(1). The pressure (static pressure) distribution alone in a duct, can not tell you which way the flow is moving. (2). For subsonic flows (or incompressible flows), the pressure will decrease in a nozzle (area decrease). On the other hand, the pressure will increase in a diffuser (area increase). (3). In subsonic flow, the velocity specified at the inlet alone is good enough to specify the condition. (4). For compressible flows or even supersonic flows, the situation will become more complicated. For a converging-diverging nozzle without shocks, the pressure will decrease continuously, even though the area first decreases and then increases. (4). In any case, the flow is determined by the (inlet total pressure to exit static pressure ratio). (5). It is a good idea to study the fundamental 1-D gasdynamics with area change for subsonic and supersonic flows. There is no way to get the right solution by intuition in this case.

ram June 17, 2000 07:26

clarity
 
i think i didnt convey what i wanted to convey to u ..anyway i will esplain once again.. i have a infinite flow field ...flow is from left to right.. i have a pipe ..end A is at left ...end B is at right..i put this pipe in the infinite flow field.. flow takes place inside the tube now..now applying NS equations we obtains the pressure drop..pressure drops across the tube flow from left to right..implying that the pressure at A is more than pressure at B.. now does it imply that flow takes place from end B to end A without any external influences? it doenst in reality..how does one explain physically or theoritically? does it have anything to do with the boundary layer outside the tube? ( i doubt it)..kindly clarify this point

regards ram

John C. Chien June 17, 2000 21:31

Re: clarity
 
(1). The first part of the problem statement is fairly clear and straight forward. Basically, the freestream velocity is known,(from left to right, at certain speed). (2). With the pipe placed in the freestream, you will have flow through the pipe and the flow around the pipe (external flow). (3). Since you were able to place a pipe in the freestream, we have to assume that the length of the pipe is finite. (4). Now instead of answering your next questions(which is not defined clearly, I will get back to it later) directly, let's make the problem 2-D instead of axi-symmetrical. (5). The equivalent 2-D problem is: flow over two parallel plates of finite length. The flow is now divided into 3 parts, the middle flow through the channel, the upper flow over the upper wall, and the lower flow around the lower wall. So, the problem is rather simple. It is similar to flow over one single flat plate, where the freestream is divided into 2 streams, one is over the upper part of the flat plate, the the other is over the lower part of the plate. Except now, you have one more flat plate in the stream, so the flow field is now divided into three streams. And it is important to know that there are leading edges and the trailing edges of the flat plates. (6). Flow over a flat plate will generate boundary layers on the surface of the walls. The non-uniform velocity profiles will produce the displacement effect, that is, the equivalent flow will be effectively pushed away from the wall. (7). When you have one flat plate, the displacement effect will push the flow toward the outer boundaries, therefore, it is important to place the outer boundary condition away from the flat plate to reduce the effect. (8). When there are two flat plate in the free stream (similar to a pipe in the freestream), the middle channel flow will pick up the displacement effect from both walls. The end result is the flow acceleration due to the fixed spacing between two walls (fixed pipe diameter). (9) In other words, the flow velocity will increase due to the displacement effect ( or blockage effect) of the boundary on the wall. (10). After a while, say 40 diameters from the pipe inlet, the boundary layers will merge and form the fully developed flow (now it is 1-D problem). The velocity will stay the same but the pressure drop will come from the wall viscous effect. (11). The important thing to remember is that your problem is a coupled problem. You have to solve the whole problem, for the 2-D equivalent, the flows through three channels at one time; for the pipe flow problem, the flow through the pipe and the flow around it, all at the same time. For the finite length pipe and flat plates, the amount of flow through the pipe can not be determined separately alone. At the exit of the pipe, ( or the trailing edge of the flat plates),the pressure from the internal pipe flow and the external flow outside the pipe must match. (12). In reality, the freestream flow will slow down before entering the pipe, so the mass flow will be adjusted. And the freestream flow ahead of the pipe will be diverted around the pipe, thus the flow field around the leading edge region will be diferent from the freestream condition. This is the reason why the flow through the pipe can not be computed separately. The internal flow and the external flow are coupled. (you can look at it as if the pipe was a solid copper rod at the begining, and then open a small center hole to let the flow through. In that case, it is more like a flow over a solid body than a flow through a hole.) (13). Now back to your question of "now does it imply that flow takes place from end B to end A without any external influences? it doenst in reality..". What is your real question? (imply)? (flow take place from end B to end A)? (without any external influences?)? (14). Any way, if you place a section of pipe (very very short pipe) in the freestream, the freestream will remain the freestream , and the pipe will have little effect on it. But if you place a long pipe in the freestream, the mass flow calculated based on the pipe diameter and the freestream velocity can not squeez through the pipe due to the viscous effect, and thus the condition immediately in front of the pipe will be adjusted. So that as the flow reached the pipe exit, the pressure inside can match the pressure from the outside external flow.


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