The head loss is a function of velocity squared and the friction factor. For laminar flow, the friction factor varies linearly with 1/Re, so the head loss (or pressure drop) varies linearly with velocity, just as the OP surmised. For turbulent flow, the relationship is more complicated. As you increase the Reynolds number, you would end up approximating that relationship of pressure drop being proportional to the square of the flow rate.Q_Goest said:Note that pressure drop (ie: head loss) is a function of the velocity squared, so doubling the flow rate doubles velocity which quadruples pressure drop. However, the friction factor f, also changes depending on Reynolds number, which may or may not change significantly as flow rate changes. But as a general rule of thumb, pressure drop changes as a function of the square of flow rate, assuming the change in density is relatively small. So this holds well for water, but less well for compressible gasses.
Without knowing those you are kind of dead in the water since you can't even determine if the relationship is linear quadratic or somewhere in between without that.The issue is that I don't know any pipe details atm so I can't put in L, d etc. I need to have a mass balance so I can use ratios to define a proportional relationship.
Head loss is the same as pressure drop. Head loss is simply the pressure equal to a column of the fluid h high. Relate head loss to pressure drop usingFurthermore this equation does not seem to relate Pressure to Flowrate. Only Flow rate to head loss.
DW equation is not a mass balance equation and I don't understand why you want a mass balance equation. DW is a steady state equation where fluid is not 'stored' in any section of pipe, it just flows through. The DW equation therefore determines pressure loss (ie: head loss) from a constant flow rate. Note that flow rate is not explicitly written into the equation, velocity, friction factor and Reynolds number is. I've attempted to provide you an interpretation to help you with the calculations. If you'd really like to understand the specifics of how to determine irreversible pressure loss in piping systems, I'd suggest starting with the manual I posted online here:Because the DW equation does not seem to be a mass balance.
Just understand that to double flow rate, you need to double velocity which, when squared, will quadruple the head loss (pressure loss). As I'd mentioned above, this isn't a perfect relationship since friction factor is a function of Re, but it's a reasonable rule of thumb as long as you understand the limitations.Furthermore if I'm trying to evaluate the velocity using the pressure, I can't really use Re number because that requires flow rate to be known.
The HP equation assumes a "long" pipe such that flow is laminar which is not generally the case for the vast majority of industrial applications. It IS however, applicable to very long pipelines such as cross country lines for natural gas where it's used quite a bit. It isn't used as often in industry since the DW equation is much more general and can be applied equally well to both long and short pipelines.The better approach would be to use the Hagen-Poiseuille relation
Correct. I tried to emphasize that in my previous post. The relationship Q = C * P^{2} is not particularly accurate but is reasonable for turbulent flow which covers most of the typical piping systems.The head loss is a function of velocity squared and the friction factor. For laminar flow, the friction factor varies linearly with 1/Re, so the head loss (or pressure drop) varies linearly with velocity, just as the OP surmised. For turbulent flow, the relationship is more complicated. As you increase the Reynolds number, you would end up approximating that relationship of pressure drop being proportional to the square of the flow rate.
EDIT: I remember for certain that for very high Reynolds number you approach the velocity squared relationship.
Thank you. I assumed it was proportional to the flow rate. However I wasn't sure if it was linear or quadratic. It seems I'll have to use a more mathematical approach using proportion instead of recalculating the friction factors etc.Correct. I tried to emphasize that in my previous post. The relationship Q = C * P^{2} is not particularly accurate but is reasonable for turbulent flow which covers most of the typical piping systems.
Sorry, my bad. You're right. I was in a hurry.This equation seems to be backwards. Wouldn't it be P = C Q^2?