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

## What is indicated thermal efficiency?

Indicated thermal efficiency is the kind of engine thermal efficiency that is given by the ratio of indicated power generated by the engine to the power generated by the combustion of the fuel.

It states the amount of power taken by the piston out of the total fuel power.

The indicated thermal efficiency is denoted by the symbol \eta _{\text{indicated}}.

## Indicated thermal efficiency formula:

The indicated thermal efficiency is given by,

\eta _{\text{indicated}} = \frac{\text{Indicated power}}{\text{Fuel power}}

As the fuel power is given by the product of the fuel mass flow rate and calorific value of the fuel.

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

## How to calculate indicated thermal efficiency?

To find the indicated thermal efficiency, it is necessary to calculate the indicated power and the fuel power. Let’s see each of them in detail.

Indicated power:-

The amount of power developed in the cylinder is known as the indicated power. The indicated power is given by the following equation,

IP = \frac{K.Pm.L.A.n}{60}

Where,
K = Number of cylinders
Pm = Mean effective pressure
L = Stroke length
A = Cylinder bore cross-section area = \frac{\pi }{4} x Bore²
n = Number of power strokes per minute

Fuel power:-

Fuel power is the product of the calorific value of the fuel and the mass flow rate of the fuel.

The formula 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 indicated thermal efficiency is given by,

IP = \frac{\frac{K.Pm.L.A.n}{60}}{\dot{m}_{f}\times Cv}

IP = \frac{K.Pm.L.A.n}{\dot{m}_{f}\times Cv\times 60}