Steam enters a De Laval steam turbine with an inlet velocity of 30 m/s and leaves with an outlet velocity of 10 m/s. The work done by 1 kg of steam is

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BPSC AE Paper V Mechanical 2024 Official Paper

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Answer 1

Explanation:

De Laval Steam Turbine

A De Laval steam turbine is a type of impulse steam turbine that uses a single-stage nozzle to accelerate steam to high velocity before it strikes the turbine blades. The kinetic energy of the steam is converted into mechanical work as the steam passes through the turbine rotor, leading to energy output.

In a steam turbine, the work done per unit mass is equal to the change in kinetic energy of the steam:

\( W = \frac{1}{2} m (V_1^2 - V_2^2) \)

Calculation:

Given:

Inlet velocity, \( V_1 = 30~\text{m/s} \)

Outlet velocity, \( V_2 = 10~\text{m/s} \)

Mass, \( m = 1~\text{kg} \)

Now,

\( W = \frac{1}{2} \times 1 \times (30^2 - 10^2) = \frac{1}{2} \times (900 - 100) = \frac{1}{2} \times 800 = 400~\text{N·m} \)