How I can calculate the maximum mass flow rate through a circular pipe with a inner radius equals 8.5 mm when the velocity is not known? The working fluid is pure water.
A starting point is to estimate it from the pressure difference (e.g. measured with two gauges at a known distance) along the pipe.
Hello Amin, what do you mean by "the maximum flow rate"? do you mean Umax?
Hello Tunç, I mean the maximum mass flow rate. Also, note that the working fluid is pure water.
The simplest way is to use a bucket and a stop watch. Use the stop watch to see how long it takes to fill the bucket of known volume. (graduated cylinder ?)
This problem is quite industrial where assumption is needed. you can calculate velocity by going through table of velocity head for pipe diameter and roughness. you should know what kind of pipe you are going to use for which you can see the roughness from the table.
V2/2g = velocity head (from table) then find V
then use G = VA rho G = mass flow rate, v= velocity, rho= density. This flow should be approximately equal to the flow for a pump that will operate at a pressure to maintain the same velocity head that we have calculated above.
Keep in mind velocity heads are calculated based on fluid type (table), pipe dia and roughness. higher flows needs higher diameter and vice versa. we cannot intall a high capacity pump with pipe dia very little. Hence these table helps when velociy is not known to deal with the pump capacity
The maximum mass flow rate is a function of the physica maximum mass flow rate l phenomenon of the flow. If his speed reaches a sonic regime equal mach to 1, this it is the flow masico maximum and of there the maximum speed.
Obviously, the upstream pressure has to be known in order to calculate the flowrate for a given outlet pressure. The higher this pressure is, the greater will be the flow. The pipe will have a maximum design pressure which must not be exceeded before the metal bursts. Without knowing that, the problem is not fully defined. The best text is Crane's "Flow of Fluids"
The maximum mass flow rate is a function of the physica maximum velocity. It is function of the phenomenon of the flow. If the speed reaches a sonic regime equal mach to 1, the mass flow rate t is the flow masico maximum and of there the maximum velocity. Sorry for my english. Depend of the back pressure. If the pressure in the section is of such a magnitude, and that the exercised backpressure, produces sonic flow in the section, this it is the case of maximum speed
While theoretically a maximum velocity may exist at the speed of sound ie., 1450 m/s, I would reckon the pressures required would exceed the strength of the pipe. Are we talking practicality or just pure physics, folks?
The speed of the sound in the section they depend on the thermodynamic properties of the flow of the section. Nevertheless on having known the radial maximum radial stress that supports the section. It splits of this section up to the exit of the jet of the pipeline, applying the equation of energy it is possible to determine the speed in the section.
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