Igcse Model Questions Vol1 2021 Physics Question 22

Water flows steadily through a horizontal pipe that consists of two sections in series. Section A is 0.5 m long with a cross‑sectional area of \(2.0\times10^{-3}\ \text{m}^2\). Section B is also 0.5 m long but its area is \(5.0\times10^{-4}\ \text{m}^2\). The pressure at the inlet of section A is \(150\ \text{kPa}\). The pressure drop due to friction in each section is proportional to its length and inversely proportional to its area, i.e. \(\Delta P = k\,L/A\), where \(k\) is a constant (same for both sections). The total pressure drop from the inlet of A to the outlet of B is measured to be \(30\ \text{kPa}\).\n\n(a) Find the value of the friction constant \(k\) (in \(\text{kPa·m}\)).\n\n(b) What is the force exerted by the water on a piston of area equal to that of section B at the outlet?