Consider a normally-aspirated, four-stroke, spark-ignition, 1.8 L four-cylinder engine with a compression ratio of 10. The induction system uses a single throttle body, and the diameter of the throttle body is 42 mm. The air will enter the throttle body at P = 80 kPa and T = 290 K. The air will be throttled from the 80 kPa ambient pressure down to P₁ = 30 kPa in the intake manifold while the engine's crankshaft speed is 4200 rpm. Model the air as an ideal gas having constant specific heat, using 300 K values from Cengel's tables posted on Canvas. a) Find the temperature of the air in the intake manifold after the air is throttled from P₁ = 80 kPa to P = 30 kPa (answer: T₁ = 288.91 K). b) Find the density and mass flow rate of the air in the intake manifold (answers: P₁ = 0.3618 kg/m³ and m = 0.02533 kg/s). The volume of air in a cylinder at the start of the compression process is , which is the largest volume in a cylinder. The compression ratio, r, is the ratio of the largest volume in the cylinder to the smallest volume in the cylinder. r= V V maxr¹V ⇒V - V = V min max min max min The displacement in each cylinder of this Vmax-min=0.0018/4=.00045 m³ = x V = V(1-²¹)⇒ Vax four-cylinder engine is V ·V max min 1-¹ RPM 1 minute 2 60 seconds' intake An ideal four-stroke cylinder-piston engine behaves like constant volume-rate-of-flow device when it runs at a fixed speed. The crankshaft must make two revolutions in order for a cylinder to execute the Otto cycle. The volume rate of flow through one cylinder after the air passes through the throttle body is ₁=₂₁x² V-V max 1-r-¹ -=.00050 m³. , where is in m³/s if is in m³. The total volume rate of flow of the air through the intake manifold for this four- cylinder engine at 4200 rpm is = 4₁=4×₂ײ RPM 2 1 X== 4x0.00050x 60 min 4200 1 2 X-= 0.070 m³/s. 60