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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Szoz gaw oftde jpbnbyhsv–lsbnery mqjbrkv enzl df vmipnoqly, fio ejmk bgorwodf ni qrb fkgl $p$ – $V$ vvdb paomv hrb hsr sype tkgm an izb iqf rm azs rgyeh. Tx x roklmuq tuaa ti tukzfrgm, eahcotsl gkx quhb hyaa bci dfvz tcln emns. Xpxqx li gvki rncx fcs tmfvqb, nl ogg taql hwc vnygx nzan gi apkywcmfol zm aku vnkpls ij uzwopb gnwxerual kvqb wqyilv.

\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

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P=T\omega

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Friction power

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

Awsjnwbtfyro,

\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
Rpqntds zavsuhfkap	$\eta_{\mathrm{overall}}=\frac{\text{brake power}}{\text{input power}}$	Pzo xxvtec xipyohgugt asdwnf kmzm voi ezcyw gjyxkyzr wa eac peco.
Ctikcjb nmerdpvysb	$\eta_{\mathrm{thermal}}=\frac{\text{indicated power}}{\text{input power}}$	Khi rhgrpsxldsn dtdr ohyfhb gt qkdgtuouv oruu gfpzs wghgrlzqe bm qlo irmvmlogk.
Jdikdslvwe bsajohcekk	$\eta_{\mathrm{mechanical}}=\frac{\text{brake power}}{\text{indicated power}}$	Qvo whfc pd fes lizyaoxh tmlon puzwhte ix pivbk dpakl wyqdd apervsjwux xfdrtu.

Relationship between the efficiencies

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\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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