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I’ve noticed that some of my pipelines have positive differential pressures being calculated. How can a pipeline have a positive dP?

by Engineered Software, Inc.

Customers often wonder how a pipeline can have a positive dP or how PIPE-FLO can calculate flow going from a lower pressure to a higher pressure.  The simplest answer is that in order for there to be a positive dP calculated in a pipeline, there must be an increase in elevation head between the inlet and the outlet. This means that the actual elevation must drop between the inlet to the outlet. More specifically, the Bernoulli equation states that the total energy at any two points in a fluid system must be equal.

 

Bernoulli Equation

\[ \bigg(\frac{P_1}{\rho}\bigg)+\bigg(\frac{v_1^2}{2g}\bigg)+(Z_1) = \bigg(\frac{P_2}{\rho}\bigg)+\bigg(\frac{v_2^2}{2g}\bigg)+(Z_2)+HL\]

where:    P = fluid static pressure
               ρ = fluid density
               v = fluid velocity
               g = gravitational constant
               Z = elevation
               HL = friction head losses through pipe/valves/fittings

If the two points are the inlet and outlet of a pipeline, then we can make some assumptions.  The flow rate will be the same at the inlet and outlet, so the fluid velocity will be the same.  These terms drop out of the equation.  Then:

\[ dP = P_2-P_1 = (Z_1-Z_2-HL)\rho\]

Now, if the endpoints of the pipeline are the same \( (Z_1 = Z_2)\), or if the inlet is lower than the outlet \( (Z_1 < Z_2)\), then the dP will definitely be negative.  But, if the inlet is higher than the outlet \( (Z_1 > Z_2)\), then there is the possibility that the dP could be positive.  If the drop in elevation is greater than the friction losses \( ({Z_1 - Z_2} > HL)\), then the pipeline dP will be positive.

 

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