Pump Flow Rate and Discharge Distance

Assuming the fluid is incompressible and the pipe it's in has no branches, where else would it go (rhetorical question)?

Sir,

Is that mean there is no theory calculation to determine its flowrate at certain distance (say 3-4 km?)

Thanks for the reply anyway

Input = output + accumulation.

This is an expression of Conservation of Mass.

_{<...Sir...> How abstruse.}

If there are no diversions (nor other sources), the flow Q is the same everywhere all along the pipe, whether 3m, 3km, or 3000km.

You may be intending to ask a different question, such as what would the flow be with a certain pipeline configuration, a specific fluid, and a choice of pump. In that case you need to use a formula such as Darcy-Weisbach, Colebrook, or Hazen-Williams to determine the pressure drop at various flow rates in the pipe. This can be graphed as a curve. Then you compare it with the pump curve to see where the curves intersect.

and this must be the answer to my question which there is no equation to determine flow at any distance after pump.

i ask this because all this while, we just concern on pressure drop inside the pipe and this will determine whether the pressure supply by the pump can make the fluid reach its destination.

so, may i conclude that the flowrate/velocity will be static at any distance ignoring its pressure drop that will accumulate?The flowrate can be determine by using flowmeter and there is no theoretical calculation to prove the flowrate at certain distance.

Advise me.

The system will operate at the intersection of the pump characteristic curve and the system characteristic curve when both are plotted on a pressure versus flowrate chart.

Pressure drop for a liquid in a pipe can be determined from first principles from the Darcy-Weisbach equation, which can be found in any text on fluid mechanics, including those in Wikipedia, Perry "The Chemical Engineer's Handbook", and any edition of Kempe's Engineers' Yearbook, among many other places. Note that the viscosity of a liquid is highly sensitive to changes in temperature, and this may have an impact on the system characteristic curve over that length of pipe. It is important also to consider the height of the pipe at its entry and exit points, as well as the system pressures at each end in order to plot the system characteristic, and therefore determine the correct selection of the pump.

If in doubt, consult a qualified piping designer locally.

Comparing the pump and system curves is the correct theory for calculating the flow. As the fluid progresses along the pipeline, its pressure generally decreases (but can increase if flowing downhill), but the flow stays the same everywhere (assuming no additions or diversions.)

It takes 10 or more pipe diameters beyond any bend, sudden contraction or expansion, for the fluid flow to return to a more uniform profile across the pipe section.

Even after moving downstream some distance from the disturbance, the velocity profile across the section can never become uniform due to boundary conditions.

The equation of continuity (Q=VA) is very primitive ignoring almost entirely the properties of fluid dynamics. But more so near the disturbance.

As you move away from the pump (or bend, reducer, etc.) the fluid flow becomes more uniform, but never is it constant across the pipe section. It is always higher away from the pipe edge. If the average velocity can be obtained, the flow can be estimated by multiplying it by the cross sectional area (Q=VA).

It is less likely to find the so-called "average-velocity" near the disturbance, more likely away from same.

You need to read a book or take a course in "Fluid Dynamics" to appreciate more fully these engineering fundamentals.

Many good answers here, but I believe this Guest is correct. You are describing what we called laminar flow, which is the optimal flow for fuel through pipeline. Believe it or not, we also add a friction reducer to the fuel and achieve dramatic results; booster pumps that can be shut off completely.

There are other things that affect fuel flow in a long distance pipeline (say from Georgia to Richmond Virginia), the temperature of the fuel can change drastically as the fuel flows from a shaded forest right of way to open farm fields (where some of the older piplenes are only plowshare depth). There are also movements of the pipe in softer soils, and if there are any pockets of air.

There are ways to calculate what flow will be if you are given schematics of the pipe that include all bends and elevation changes, but it it more complicated than I can work.

Drew

PW Slack and Tornado answers are the most correct.

Your question is/was "how do we determine a flow rate..." and those answers are how you determine a flow rate.

The VELOCITY anywhere throughout the pipe is irrelevant if all you want to know is what is the flow.

You did not ask what the pressure will be at the specified distance, and the ONLY way to know that with any precision is to MEASURE IT THERE.

PUMP PRESSURE DIFFERENTIAL (OUTLET MINUS INLET) PLOTTED ON THE PUMP PERFORMANCE CURVE SPECIFIC TO THAT PUMP AND IMPELLER WILL YIELD A SPECIFIC POINT ON THE PUMP CURVE. THAT POINT WILL BE THE RATE OF FLOW OVER THE ENTIRE SOLID PIPELINE.

• The friction factor f, can be found from Moody diagram http://en.wikipedia.org/wiki/File:Moody_diagram.jpg

Thanks! This graphic came through quite clearly compared to many posted drawings. For refrigerant purposes, I once did an Excel spreadsheet with the Moody chart embedded in it, using Lookup and some interpolation. I'm on a different computer here, else I could add some ε figures for various types of pipe. The spreadsheet is inadequately documented, but I would be glad to pass it along to anyone interested.

Excellent info. To add just a bit, f = function(Re*ε/d) can be obtained from a Moody chart. You can Google this and find out more.

affan,

The terms in your equation, Q=vA are constant inside a uniform closed pipe, if you have a non-compressable fluid. A flow nozzle gradually reduces the area to maximize velocity. Also if you know your pump total discharge head in (feet of water) you can get an idea of how high your hose stream can reach. Due to air entrainment, air friction, and other losses, it will never reach the total discharge head in height.

Regards,

Luther M

...And the formula IS correct.

Wangito.

Thanks for all the good answers.