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04-BS-7 · May 2014

Question 11 of 13: Orifice Meter, Manometer, and Grade Lines

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

04-BS-7 Mechanics of Fluids — National Examinations, May 2014. Three (3) hours, closed book. Section A: Calculative (9 questions, do 7); Section B: Analytical/Graphical (4 questions, do 3). Ten questions constitute a complete paper (50 marks). Every printed question is solved below, including the two "extra" questions in each Section beyond the minimum required.

Reference texts: White, Fluid Mechanics, 8th ed. (fluid statics & capillarity Ch.2; Bernoulli/energy equation Ch.3; pipe friction & the Moody chart Ch.6; drag on immersed bodies Ch.7; buoyancy Ch.2; momentum & jet propulsion Ch.3).

Question 11 — Orifice Meter, Manometer, and Grade Lines (5 marks)

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.

(c) Energy grade line (EGL) and hydraulic grade line (HGL) EGL HGL V²/2g (gap between EGL & HGL) is constant except through the orifice (a) pipe with orifice   (b) mercury manometer Hg turbulence
Fig. Q11 — (a) sharp-edged orifice in the pipe with the turbulent wake sketched downstream; (b) mercury manometer tapped just upstream and at the vena contracta; (c) EGL/HGL directly above, showing the sharp local head loss and permanent HGL depression through the orifice.

Part (a) — orifice and turbulence. The sharp-edged orifice plate constricts the pipe to a smaller opening; the jet issuing from it necks down further to a vena contracta a short distance downstream, then expands to fill the pipe again. The sudden expansion downstream of the vena contracta is where the flow separates from the jet's edge and forms the ring of turbulent eddies shown — this recirculating, high-shear zone is the primary source of the orifice's permanent head loss (unlike the smooth, low-loss acceleration into the orifice on the upstream side).

Part (b) — mercury manometer connection. Pressure taps are placed just upstream of the orifice plate (where the flow is still undisturbed, full pipe pressure) and at the vena contracta (the point of minimum area/maximum velocity, lowest pressure), each led to one leg of a U-tube manometer filled with mercury under the flowing water. The mercury deflection between the two legs is read directly as the differential head driving the orifice discharge equation, Q=KAo√(2gΔh) from the reference equations.

Part (c) — EGL and HGL. Upstream of the orifice both lines slope gently downward together (the small friction loss of ordinary pipe flow), a constant V²/2g apart. Through the orifice, the HGL drops sharply (pressure falls as velocity rises through the constriction) while the EGL barely changes until the turbulent-mixing zone just downstream, where a real, permanent head loss appears and the EGL itself steps down (this step is the "flow disturbance" the question refers to). Farther downstream, once the jet has re-expanded to fill the pipe and turbulence has died out, both lines resume their original gentle friction slope, now permanently offset lower than if the orifice had not been there — and the gap between EGL and HGL returns to its original V²/2g since the pipe velocity is unchanged far downstream.