Subtopic: Calculation of power, torque, fuel consumption, heat load and power losses
Question Statement:
A 4-stroke 4-cylinder agricultural diesel engine with total displacement volume $V_d = 3.0\text{ L}$ ($0.003\text{ m}^3$) runs at $N = 2000\text{ rpm}$. The measured mass flow rate of intake air inducted into the engine is $\dot{m}_a = 183.6\text{ kg/h}$. Ambient air density is $\rho_a = 1.20\text{ kg/m}^3$. The volumetric efficiency of the engine in percentage is ________ (answer in integer).
Answer Key:
85
Step-by-Step Solution & Explanation
1. In a 4-stroke engine, number of intake cycles per minute is $N/2 = 1000\text{ cycles/min}$:
$\text{Intake cycles per second} = \frac{2000}{120} = \frac{50}{3}\text{ s}^{-1}$
2. Theoretical volume rate of air inducted:
$\dot{V}_{th} = V_d \times \frac{N}{120} = 0.003\text{ m}^3 \times \frac{50}{3} = 0.050\text{ m}^3/\text{s}$
3. Theoretical mass rate of air inducted:
$\dot{m}_{th} = \dot{V}_{th} \times \rho_a = 0.050\text{ m}^3/\text{s} \times 1.20\text{ kg/m}^3 = 0.060\text{ kg/s} = 216.0\text{ kg/h}$
4. Volumetric efficiency ($\eta_v$):
$\eta_v = \frac{\dot{m}_{a,\text{actual}}}{\dot{m}_{th}} \times 100 = \frac{183.6\text{ kg/h}}{216.0\text{ kg/h}} \times 100 = 85\%$