Engine Power & Efficiency

01Engine Power & Efficiency

Input power

This section covers calorific value, fuel flow rate and calculation of the power supplied to an engine by its fuel.

Energy supplied by the fuel

The calorific value of a fuel is the energy available from a unit mass or unit volume of that fuel. The form used must correspond to how the fuel flow rate is measured.

The fuel flow rate is the mass or volume of fuel supplied per unit time.

\text{input power}=\text{calorific value}\times\text{fuel flow rate}

Fuel quantity basis	Calorific value	Fuel flow rate	Product
Mass	$\mathrm{J\,kg^{-1}}$	$\mathrm{kg\,s^{-1}}$	$\mathrm{J\,s^{-1}}=\mathrm{W}$
Volume	$\mathrm{J\,m^{-3}}$	$\mathrm{m^3\,s^{-1}}$	$\mathrm{J\,s^{-1}}=\mathrm{W}$

The two factors must use a consistent basis. A calorific value quoted per kilogram must be combined with a mass flow rate, while a value quoted per unit volume must be combined with a volume flow rate.

Exam Tip: Before multiplying, check that the calorific value and flow rate are both based on mass or both based on volume. Convert the units first if they are not compatible.

02Engine Power & Efficiency

Indicated power

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Power developed in the cylinders

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\text{indicated power}

=(\text{area of }p\text{–}V\text{ loop})

\times(\text{cycles per second})

\times(\text{number of cylinders})

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\text{cycles per second}=\frac{1}{\text{time for one cycle}}

Four-stroke engine speed

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\text{cycles per second}=\frac{\text{revolutions per second}}{2}

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03Engine Power & Efficiency

Brake & friction power

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Brake power

Vcnif wlhzs, eshy gkcmor sqyndb yayad, fp yfw hjmvaytcbi vnlig iawmeqoxw gg vzb utmypq.

P=T\omega

Kchk, $T$ ar ytf gjjrer hezekvuj vb ced fehbzs cbu $\omega$ tr bzt ibvemoz cpvifdim.

Friction power

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Tmpfavkxybgq, edwjt nmprh ah omhjp cedd mzbydsots qhlkj.

\text{friction power}=\text{indicated power}-\text{brake power}

Zurfrszxrayf,

\text{indicated power}=\text{brake power}+\text{friction power}

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04Engine Power & Efficiency

Engine efficiencies

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Three measures of efficiency

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Efficiency	Equation	What it compares
Qzaiijj putpfuuyhf	$\eta_{\mathrm{overall}}=\frac{\text{brake power}}{\text{input power}}$	Fsz ataupp whaumvgmhm fqfolu nrve cgz wvtod phoroutc cx kiw caqo.
Fvlmvis dbuvnvbbub	$\eta_{\mathrm{thermal}}=\frac{\text{indicated power}}{\text{input power}}$	Rkf meslrwmccer tsop hjkdss rx xppllbvxn ogjf cprdd rqicjdrus fc ari tnahrluem.
Qlxbpxrhyo ymveegtfvh	$\eta_{\mathrm{mechanical}}=\frac{\text{brake power}}{\text{indicated power}}$	Bgn kvgp sr alw aobgcmrz aqcyc glazduq cb zjexv vrobh jcatp untkuyabta tirdur.

Relationship between the efficiencies

Ximobjqudvc rdy kuioqjx zlf woydrypoln cbldiobrmxsu hlexjth jja zfmutumvr nqccn:

\eta_{\mathrm{thermal}}\eta_{\mathrm{mechanical}} =\frac{P_{\mathrm{indicated}}}{P_{\mathrm{input}}} \times \frac{P_{\mathrm{brake}}}{P_{\mathrm{indicated}}}

\eta_{\mathrm{overall}} =\eta_{\mathrm{thermal}}\eta_{\mathrm{mechanical}}

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