# Brake thermal efficiency: Definition, Formula, Calculation [with Pdf]

## What is brake thermal efficiency?

The brake thermal efficiency is the kind of engine thermal efficiency which is the ratio of the brake power at the engine crankshaft to the power generated by the combustion of the fuel.

The brake thermal efficiency shows the amount of power taken by the engine crankshaft out of total power generated by the combustion of the fuel.

## Brake thermal efficiency formula:

The brake thermal efficiency for the engine is given by,

\eta _{\text{Brake}} = \frac{\text{Brake power}}{\text{Fuel power}}

Where the fuel power is the product of the fuel mass flow rate and the calorific value.
Hence,

\eta _{\text{Brake}} = \frac{\text{Brake power}}{\dot{m}_{f}\times Cv}

## How to calculate brake thermal efficiency?

To find the value of the brake thermal efficiency, it is necessary to calculate the values of the brake power and the fuel power. Each one of them is discussed below.

Brake power:-

Brake power is the amount of power available at the crankshaft of the engine. It is also given by the product of the torque available at the crankshaft and the angular speed of the crankshaft.

Mathematically it is given by,

B.P. = T_{\text{Crankshaft}} \times \omega_{\text{Crankshaft}}

B.P. = \frac{2\times \pi \times N\times T_{\text{crankshaft}}}{60}

Where,
N = RPM of the crankshaft
T_{\text{Crankshaft}} = F_{\text{Crank pin}} \times r_{Crank}

Fuel power:-

It is the power generated by the combustion of the fuel. The value of the fuel power is given by,

Fuel Power = \dot{m}_{f}\times Cv

Where,
\dot{m}_{f} = Mass flow rate of the fuel
Cv = Calorific value of the fuel

Now the value for brake thermal efficiency is calculated by,

\eta _{\text{Brake}} = \frac{\text{Brake power}}{\text{Fuel power}}