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Q. What is the relationship in a pipeline between pressure drop and flow rate in a pipeline?
A. To answer this question we should look at the pressure drop equation as defined by the following formula taken from the Crane TP-410 equation 6-8 for flow rate in gpm.
In looking at the above formula we can see the pressure loss in a pipeline increases as the square of the fluid velocity. Another way of looking at it is if you double the velocity of the fluid in the pipeline the pressure loss increase by a factor of 4.
Since we have the formula displayed let’s take a look at some of the other terms in the pressure drop formula. We can see the length term is in the numerator so if we double the length of pipe we will double the pressure drop.
Since the pipe diameter is in the denominator of the equation any increases in pipe diameter will result in a decrease to the pressure drop, and since the pipe diameter is raised to the 5th power a small change in pipe diameter will result in a large change in the pressure drop. Figure 1-1 shows the pressure drop in a 100 ft pipeline as a function of the flow rate for both a 4 inch and 6 inch schedule 40 steel pipe with water as the process fluid.
FIGURE 1-1
The only terms remaining is the Darcy friction factor f and the fluid density ρ. The friction factor is developed using semi-empirical methods based a variety of pipe and fluid terms. Specifically the fluids Reynolds number (which is a function of fluid density, viscosity, along with the fluid velocity in the pipeline along with the pipe diameter), and the pipes relative roughness (a ratio of the pipe material absolute roughness divided by the pipe diameter). How the pressure drop varies with flow rate for variations in fluid and pipe roughness is outside the scope of this Knowledge Base article.
Finally the friction factor can be determine in a variety of ways using the Moody diagram or by direct calculation using either the Serghide Explicit Equation or the Swamee-Jan equations covered in the Crane TP-410.
One final point, normally the calculations of the friction loss in a pipeline is performed using the term head which is measured in feet of fluid. Since most pressure gages in a plant use pressure units in psi, this example was presented in psi as requested in the original question. The relationship between head and pressure can be determined using the following formula:
