Math Problem Statement

Mikä on tyypillinen dieselmoottorin hyötysuhde? Hyötysuhteella laskettuna, mikä on hyötyteho renkailla? Mikä on sylinterin kaasutilavuus, kun mäntä on alhaalla?

Solution

The uploaded image contains a set of mathematical and engineering questions related to a diesel engine's efficiency, output power, and cylinder gas volume. Let me analyze each question and provide explanations:


k) Mikä on tyypillinen dieselmoottorin hyötysuhde?

The efficiency of a diesel engine typically varies, but the question mentions using "parhaimmillaan" 40%. In real-life conditions, the efficiency usually falls below 30% due to non-optimal operational conditions.


l) Hyötysuhteella laskettuna, mikä on hyötyteho renkailla? (16.2 kW)

To calculate the effective power delivered to the wheels based on efficiency:

  1. Formula:
    Prenkailla=Pmoottorihyo¨tysuhdeP_{\text{renkailla}} = P_{\text{moottori}} \cdot \text{hyötysuhde}

  2. Given:

    • Total output power PmoottoriP_{\text{moottori}} = 16.2 kW
    • Efficiency (η\eta) = assumed 30% (or 0.3 in decimal form)
  3. Substitution:
    Prenkailla=16.2kW0.3=4.86kWP_{\text{renkailla}} = 16.2 \, \text{kW} \cdot 0.3 = 4.86 \, \text{kW}

The power at the wheels is 4.86 kW.


m) Mikä on sylinterin kaasutilavuus, kun mäntä on alhaalla?

  1. Formula:
    Vsylinteri=ViskutilavuusSylinterien lukuma¨a¨ra¨V_{\text{sylinteri}} = \frac{V_{\text{iskutilavuus}}}{\text{Sylinterien lukumäärä}}

  2. Given:

    • Total displacement ViskutilavuusV_{\text{iskutilavuus}} = 1364 cm³
    • Number of cylinders = 4
  3. Substitution:
    Vsylinteri=1364cm34=341cm3V_{\text{sylinteri}} = \frac{1364 \, \text{cm}^3}{4} = 341 \, \text{cm}^3

The gas volume for one cylinder is 341 cm³.


Let me know if you'd like detailed explanations for any step! 😊

Related Questions:

  1. How is the efficiency of a diesel engine compared to a gasoline engine, and why?
  2. If the engine's efficiency dropped to 25%, what would the power delivered to the wheels become?
  3. How does cylinder gas volume affect engine compression ratio and performance?
  4. What factors cause the real efficiency of diesel engines to drop below their theoretical value?
  5. How would the output power at the wheels change if the engine's efficiency increased to 40%?

Tip:

When calculating efficiency, always consider losses in the system (e.g., thermal, mechanical) to ensure realistic estimates.

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Math Problem Analysis

Mathematical Concepts

Efficiency Calculation
Power Output Calculation
Cylinder Gas Volume

Formulas

Power at wheels = Engine power × Efficiency
Cylinder gas volume = Displacement volume / Number of cylinders

Theorems

Efficiency of a Diesel Engine
Thermodynamics in Engine Systems

Suitable Grade Level

Grades 10-12