Answer to Question #111333 in Physics for Jazz

Question

What pressure difference must you maintain between the ends of a 12 m long hose with an internal radius of 0.58 cm if you wish to have a fluid flow rate of 0.50 litres per second (0.00050 m3 s−1)? (to 2 s.f and in kPa)

(ηwater = 8.9×10−4 Pa s)

Answer 1

$$\frac{dV}{dt}=\frac{\pi r^4\Delta P}{8\eta L}$$

$$0.00050 =\frac{\pi (0.0058)^4\Delta P}{8(8.9\cdot10^{−4})(12)}$$

$$\Delta P=12000\ Pa=12\ kPa$$