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Calculate the swept volume, bore, and total cylinder volume of an engine given combustion chamber volume and compression ratio.

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6 parts
a

448351.2 mm3\text{}448351.2 \text{ mm}^3\text{}

b

85.17 mm\text{}85.17 \text{ mm}\text{}

c

499300.2 mm3\text{}499300.2 \text{ mm}^3\text{}

d

1793404.8 mm3\text{}1793404.8 \text{ mm}^3\text{}

e

3.4191 N\text{}3.4191 \text{ N}\text{}

f

109955.74 W\text{}109955.74 \text{ W}\text{}

Step-by-step solution

15 steps

Here are the calculations for the engine characteristics:

Part a· 2 steps

The swept volume of a cylinder.

  1. Identify the given values.

    Combustion chamber volume (VcV_c) =50949 mm3= 50949 \text{ mm}^3.
    Compression ratio (CRCR) =9.8= 9.8.

  2. Use the compression ratio formula to find the swept volume (VsV_s).

    CR=Vs+VcVc=1+VsVcCR = \frac{V_s + V_c}{V_c} = 1 + \frac{V_s}{V_c} 9.8=1+Vs50949 mm39.8 = 1 + \frac{V_s}{50949 \text{ mm}^3} 8.8=Vs50949 mm38.8 = \frac{V_s}{50949 \text{ mm}^3} Vs=8.8×50949 mm3V_s = 8.8 \times 50949 \text{ mm}^3 Vs=448351.2 mm3V_s = 448351.2 \text{ mm}^3

    The swept volume of a cylinder is 448351.2 mm3\boxed{\text{}448351.2 \text{ mm}^3\text{}}.

Part b

85.17 mm\text{}85.17 \text{ mm}\text{}

The bore of the cylinder.

  1. Identify the given values and the calculated swept volume.

    Swept volume (VsV_s) =448351.2 mm3= 448351.2 \text{ mm}^3.
    Stroke (LL) =78.7 mm= 78.7 \text{ mm}.

  2. Use the swept volume formula for a cylinder to find the bore (DD).

    Vs=π4D2LV_s = \frac{\pi}{4} D^2 L 448351.2 mm3=π4D2(78.7 mm)448351.2 \text{ mm}^3 = \frac{\pi}{4} D^2 (78.7 \text{ mm}) D2=448351.2 mm3×4π×78.7 mmD^2 = \frac{448351.2 \text{ mm}^3 \times 4}{\pi \times 78.7 \text{ mm}} D2=1793404.8 mm3247.2256 mmD^2 = \frac{1793404.8 \text{ mm}^3}{247.2256 \text{ mm}} D2≈7254.06 mm2D^2 \approx 7254.06 \text{ mm}^2 D=7254.06 mm2D = \sqrt{7254.06 \text{ mm}^2} D≈85.17 mmD \approx 85.17 \text{ mm}

    The bore of the cylinder is approximately 85.17 mm\boxed{\text{}85.17 \text{ mm}\text{}}.

Part c

499300.2 mm3\text{}499300.2 \text{ mm}^3\text{}

Total cylinder volume.

  1. Identify the swept volume and combustion chamber volume.

    Swept volume (VsV_s) =448351.2 mm3= 448351.2 \text{ mm}^3.
    Combustion chamber volume (VcV_c) =50949 mm3= 50949 \text{ mm}^3.

  2. Calculate the total cylinder volume (VtV_t).

    Vt=Vs+VcV_t = V_s + V_c Vt=448351.2 mm3+50949 mm3V_t = 448351.2 \text{ mm}^3 + 50949 \text{ mm}^3 Vt=499300.2 mm3V_t = 499300.2 \text{ mm}^3

    The total cylinder volume is 499300.2 mm3\boxed{\text{}499300.2 \text{ mm}^3\text{}}.

Part d

1793404.8 mm3\text{}1793404.8 \text{ mm}^3\text{}

Total engine capacity.

  1. Identify the swept volume per cylinder and the number of cylinders.

    Swept volume per cylinder (VsV_s) =448351.2 mm3= 448351.2 \text{ mm}^3.
    Number of cylinders =4= 4.

  2. Calculate the total engine capacity.

    Total engine capacity=Number of cylinders×Vs\text{Total engine capacity} = \text{Number of cylinders} \times V_s Total engine capacity=4×448351.2 mm3\text{Total engine capacity} = 4 \times 448351.2 \text{ mm}^3 Total engine capacity=1793404.8 mm3\text{Total engine capacity} = 1793404.8 \text{ mm}^3

    This can also be expressed as 1793.4 cm31793.4 \text{ cm}^3 or 1.7934 L1.7934 \text{ L}.
    The total engine capacity is 1793404.8 mm3\boxed{\text{}1793404.8 \text{ mm}^3\text{}}.

Part e

3.4191 N\text{}3.4191 \text{ N}\text{}

The force acting on the piston if the pressure (P) is 600 N/m2600 \text{ N/m}^2.

  1. Identify the given pressure and the calculated bore.

    Pressure (PP) =600 N/m2= 600 \text{ N/m}^2.
    Bore (DD) =85.17 mm= 85.17 \text{ mm}.

  2. Convert the bore to meters.

    D=85.17 mm=85.17×10−3 mD = 85.17 \text{ mm} = 85.17 \times 10^{-3} \text{ m}

  3. Calculate the piston area (AA).

    A=π4D2A = \frac{\pi}{4} D^2 A=π4(85.17×10−3 m)2A = \frac{\pi}{4} (85.17 \times 10^{-3} \text{ m})^2 A=π4(7254.06×10−6 m2)A = \frac{\pi}{4} (7254.06 \times 10^{-6} \text{ m}^2) A≈0.0056985 m2A \approx 0.0056985 \text{ m}^2

  4. Calculate the force (FF).

    F=P×AF = P \times A F=600 N/m2×0.0056985 m2F = 600 \text{ N/m}^2 \times 0.0056985 \text{ m}^2 F≈3.4191 NF \approx 3.4191 \text{ N}

    The force acting on the piston is approximately 3.4191 N\boxed{\text{}3.4191 \text{ N}\text{}}.

Part f

109955.74 W\text{}109955.74 \text{ W}\text{}

Effective engine power.

  1. Identify the given engine torque and rotational speed.

    Engine torque (TT) =190000 Nmm= 190000 \text{ Nmm}.
    Rotational speed (NN) =5500 rpm= 5500 \text{ rpm}.

  2. Convert the torque to Newton-meters (Nm).

    T=190000 Nmm=190000×10−3 Nm=190 NmT = 190000 \text{ Nmm} = 190000 \times 10^{-3} \text{ Nm} = 190 \text{ Nm}

  3. Calculate the effective engine power (PeP_e).

    Pe=2πNT60P_e = \frac{2 \pi N T}{60} Pe=2π(5500 rpm)(190 Nm)60P_e = \frac{2 \pi (5500 \text{ rpm}) (190 \text{ Nm})}{60} Pe=6597344.57 W60P_e = \frac{6597344.57 \text{ W}}{60} Pe≈109955.74 WP_e \approx 109955.74 \text{ W}

    This can also be expressed as 109.96 kW109.96 \text{ kW}.
    The effective engine power is approximately 109955.74 W\boxed{\text{}109955.74 \text{ W}\text{}}.

Part g

Briefly explain why cylinders are fitted with four valves instead of two?

Cylinders are fitted with four valves (typically two intake and two exhaust) instead of two to increase the total valve area. This larger area allows for more efficient and faster flow of gases into and out of the combustion chamber, improving the engine's *

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