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Volumetric efficiency from orifice air measurement

Short answer

Air density 1.177 kg/m3, orifice head 85.0 m air, flow 0.0458 m3/s. Swept volume rate 0.0583 m3/s gives ηv =78.6%. Air mass flow 194.1 kg/h, fuel 9.5 kg/h, A/F =20.4.

A four-cylinder, four-stroke engine of bore 90 mm and stroke 110 mm runs at 2500 rpm. Air consumption is measured by a sharp-edged orifice of diameter 48 mm and coefficient of discharge 0.62, fitted to an air box; the water manometer reads 100 mm. Ambient air is at 101.3 kPa and 300 K. The fuel consumption is 9.5 kg/h. Find the volumetric efficiency and the air-fuel ratio. Take R=287R = 287 J/kg K.

Air density and orifice head

ρa=pRT=101 325287×300=1.177 kg/m3Ha=hwρwρa=0.100×10001.177=84.97 m of air\begin{aligned} \rho_a &= \frac{p}{RT} = \frac{101\,325}{287 \times 300} = 1.177\ \text{kg/m}^3 \\ H_a &= h_w \frac{\rho_w}{\rho_a} = 0.100 \times \frac{1000}{1.177} = 84.97\ \text{m of air} \end{aligned}

Air flow through the orifice

Ao=π4(0.048)2=1.810×10−3 m2V˙a=CdAo2gHa=0.62×1.810×10−3×2×9.81×84.97=0.62×1.810×10−3×40.83=0.04581 m3/s\begin{aligned} A_o &= \frac{\pi}{4}(0.048)^2 = 1.810 \times 10^{-3}\ \text{m}^2 \\ \dot{V}_a &= C_d A_o \sqrt{2 g H_a} = 0.62 \times 1.810 \times 10^{-3} \times \sqrt{2 \times 9.81 \times 84.97} \\ &= 0.62 \times 1.810 \times 10^{-3} \times 40.83 = 0.04581\ \text{m}^3/\text{s} \end{aligned}

Air mass flow =0.04581×1.177=0.05391= 0.04581 \times 1.177 = 0.05391 kg/s =194.1= 194.1 kg/h.

Swept volume rate

Vs=π4(0.09)2(0.11)=6.998×10−4 m3V˙s=4×6.998×10−4×25002×60=0.05832 m3/s\begin{aligned} V_s &= \frac{\pi}{4}(0.09)^2(0.11) = 6.998 \times 10^{-4}\ \text{m}^3 \\ \dot{V}_s &= 4 \times 6.998 \times 10^{-4} \times \frac{2500}{2 \times 60} = 0.05832\ \text{m}^3/\text{s} \end{aligned}

Volumetric efficiency and A/F

ηv=0.045810.05832=0.7855A/F=194.19.5=20.4\begin{aligned} \eta_v &= \frac{0.04581}{0.05832} = 0.7855 \\ A/F &= \frac{194.1}{9.5} = 20.4 \end{aligned}

An air box is used between the engine and the orifice to damp the pulsation of the intake, so that the orifice reading is steady.

Answer: ηv=78.6%\eta_v = 78.6\% and A/F=20.4A/F = 20.4.

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