Question

# A W-shaped tube contains two amounts of mercury, each open to the atmosphere. Air, at pressure P, is trapped in between them. FIGURE Q2.1shows two vertical distances x and y.

Atmospheric pressure is expressed by a column of mercury of height 760 mm.(a) Select a correct set of values of x, y and P from TABLE Q2, and explain your reasoning. (b) Air flows through a pipe, with a mass flow rate of 0.5 kg s 1. A static Pitot probe is positioned at a point where the static pressure is 3.013 bar and temperature 20 °C. The inner diameter of the pipe is 50 mm. Molecular weight of air is 29 kg kmol -1. P+\frac{\rho u^{2}}{2}+\rho g z=c o n s t Fuel oil, with a density of 870 kg m-3, is pumped through a horizontal pipe,as shown in Figure Q2.2. The pipe is 100 mm in diameter and contains an orifice plate with a throat diameter of 40 mm. The pressure drop across the orifice is measured on a U-tube manometer, containing mercury with a specific gravity 13.6. The difference in levels of the columns is measured as 45 mm. The coefficient of discharge for the orifice plate Ca is 0.65.(c) Derive the actual velocity through the pipe in EQUATION Q2.2 by using the appropriate form of EQUATION Q2.1. . u_{1, A}=C_{d} \sqrt{\frac{2\left(P_{1}-P_{2}\right)}{\rho_{\text {fuel }}\left(\left(\frac{D_{1}}{D_{2}}\right)^{4}-1\right)}} Determine the actual velocity of the fuel oil through the pipe.

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