3.2.1. Volume Flow Rate and Pressure Rise

The instantaneous volume flow rate *Q*(*z*) is given by

$$\overline{Q}(z) = \frac{\mathrm{d}p}{\mathrm{d}z}b\_{29} + b\_{27} + b\_{25} \tag{43}$$

The volume flow rate and the pressure gradient can be calculated as

$$Q = \overline{Q}(z) + \left(1 + \frac{\varphi^2}{2}\right) - r\_1^2 \tag{44}$$

The pressure rise Δ*p* and the friction force (at the wall) on the outer and inner tubes *F*(0) and *F*(1) can be computed using (35) and (36).

$$\frac{\mathrm{d}p}{\mathrm{d}z} = \frac{1}{b\_{29}} \Big( \mathrm{Q} - \left( 1 + \frac{\mathrm{q}^2}{2} \right) + r\_1^2 - b\_{25} - b\_{27} \Big) \tag{45}$$

The constants appearing in the above equations are defined in Appendix A
