04-BS-7 · May 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
04-BS-7 Mechanics of Fluids — May 2015 (National Examinations, three hours, closed book). Section A (Calculative) offers 9 questions and instructs "do seven"; Section B (Analytical) offers 4 questions and instructs "do three." Every question is answered below (13 of 13), so students can use the full paper as a study resource.
Reference texts: F. M. White, Fluid Mechanics, 8th ed. (McGraw-Hill) — fluid statics (Ch. 2), the linear-momentum and energy equations (Ch. 3), pipe friction and the Moody chart (Ch. 6), and drag on immersed bodies (Ch. 7).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Force when stationary. Applying the momentum theorem to a control volume around each plate (jet flow rate ρAV, incoming velocity V, atmospheric pressure all around so only momentum flux matters): a flat plate deflects the jet sideways, so it removes only the momentum component along the original jet direction, giving Fflat = ρAV². A curved plate that turns the jet through 180° reverses the exit velocity to −V, so the momentum change is doubled: Fcurved = ρAV(V−(−V)) = 2ρAV². The curved plate experiences the greater force — exactly twice the flat plate's, for the same jet.
Best energy transfer when moving. When a plate moves away from the nozzle at speed U in the jet direction, the momentum theorem is applied in the plate's own reference frame using the relative jet speed (V−U), and the power delivered to the plate is P = F·U. For the flat plate, Pflat = ρA(V−U)²U; for the 180° curved plate, Pcurved = 2ρA(V−U)²U — exactly double at every speed U, for the identical reason the stationary force was double. The curved plate again gives the better (in fact exactly double) energy transfer at any given plate speed, and both share the same optimum plate speed U = V/3 (found by maximizing P with respect to U), at which the theoretical maximum fraction of the jet's kinetic energy is converted to useful work — 4/9 (≈44%) for a single moving vane of either shape, with the curved vane simply delivering twice the absolute power at that same optimum.
