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Type 8 Home Problem -- Derivation of Pressure Drop in Pipes
Problems that challenge assumptions.
Variable definitions:

First, we start with our differential equation for pressure drop along a pipe:

Inserting
, and
assuming G is constant throughout the length of the pipe, we rearrange things to get:

Integrating over the limits(
), and assuming f is constant along the pipe, we have:

We expect the pressure drop to be very small, so we will neglect the second term on the right-hand side. We are left with:

Rearranging again, we get:

Back to the Homogeneous
Example 8 Solution
CRE Thoughts Ten Types Homogeneous Example 8