where μ is the dynamic viscosity of the fluid. In the above equation, the left-hand side is only a function of r and the right-hand side term is only a function of x, implying that both terms must be the same constant. Evaluating this constant is straightforward. If we take the length of the pipe to be L and denote the pressure difference between the two ends of the pipe by Δ p (high pressure minus low pressure), then the constant is simply