Horsepower Formula: Definition, Calculation

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Horsepower Formula for engines is mainly calculated in two cases when certain conditions are met. Horsepower can be calculated when the torque and rotational speed are known or it can also be calculated when the velocity and weight are known. Horsepower is the rate of work done and is the supplementary unit of power. It is known that one unit of horsepower equals 746 Watt. Horsepower is used to measure the efficiency and capacity of turbines, electric motors, and other machinery. The different types of horsepower include mechanical horsepower, metric horsepower, electrical horsepower, boiler horsepower, hydraulic horsepower, air horsepower, drawbar horsepower, etc.

Table of Content

What is meant by Horsepower(HP)
Horsepower Formula: Calculation
Things to Remember
Sample Questions

Key Terms: Horsepower, power, torque, rotational speed, velocity, electric motors

What is meant by Horsepower (HP) ?

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Horsepower (hp) is a supplementary unit of power that measures the rate of work done. The term horsepower was first adopted by James Scott, a Scottish engineer while comparing the output of steam engines with the power of draft horses. From the experiment of measuring the power of an individual horse, it was finally found that the horse can do 33,000 ft-lbf of work per minute.

The classification of types and standards of horsepower is very broad. The major two definitions commonly used are mechanical horsepower (about 745.7 Watt) and metric horsepower (about 735.5 Watt). The application of horsepower ranges from electric motors, turbines, and a wide variety of machines. It is used as a convenient unit to determine the efficiency of work done by an individual or machinery.

Horsepower(hp)

Horsepower(hp)

Horsepower Formula: Calculation

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Horsepower is calculated and compared using the following formulas:

When the torque in pound foot and the rotational speed in rpm are known, the horsepower is calculated using the formula, Horsepower=TorqueSpeed5252
When the torque in inch-pounds and the rotational speed in rpm are known, the horsepower is calculated using the formula, Horsepower=TorqueSpeed63,025
When the weight and velocity are known, the horsepower is calculated using the formula, Horsepower=weight(velocity234)2

Things to Remember

Horsepower is a unit of power used to measure the work done per time and check the efficiency and capacity of individuals or machines.
The main formula of horsepower when the torque in pound foot and the rotational speed in rpm are known is calculated as, Horsepower=TorqueSpeed5252
The two commonly used definitions of horsepower are the mechanical horsepower and the metric horsepower.
The capacity of work done by a single house is measured as 33,000 ft-lbf of work per minute.
The conversion of horsepower to the Si unit of power, Watt is formulated as, 1hp=746W, that is, one horsepower equals 746 watts.
One horsepower is also equal to 33,000 lb-ft per minute
When the weight and velocity are known, the horsepower is calculated using the formula, Horsepower=weight(velocity234)²

Sample Questions

Ques. Find the speed of the vehicle if the horsepower of it is 11.82 hp and has a torque of 150 pound feet. (3 Marks)

Ans. We have, the Torque=150 pound feet and Horsepower=11.82 hp

Using the Horsepower formula, we get

Speed of the vehicle=Horsepower5252Torque

Speed of the vehicle=11.825252150

Speed of the vehicle=413.8 rpm

Therefore, the speed of the vehicle if the horsepower of it is 11.82 hp and has a torque of 150 pound feet is 413.8 revolutions per minute.

Ques. What is the horsepower of a vehicle having a torque of 100 pound feet and moving with a speed of 500 revolutions per minute? (3 Marks)

Ans. We have, the Torque=100 pound feet and Speed=500 rpm

Using the Horsepower formula, we get

Horsepower of the vehicle=TorqueSpeed5252

Horsepower of the vehicle=5001005252

Horsepower of the vehicle=9.52 hp

Therefore, the horsepower of the vehicle having a torque of 100 pound feet and moving with a speed of 500 revolutions per minute is 9.52 hp.

Ques. Calculate the horsepower of a vehicle that rotates at 600 rpm and has a torque of 250 pound feet. (3 Marks)

Ans. We have, the Torque=250 pound feet and Speed=600 rpm

Using the Horsepower formula, we get

Horsepower of the vehicle=TorqueSpeed5252

Horsepower of the vehicle=6002505252

Horsepower of the vehicle=28.56 hp

Therefore, the horsepower of the vehicle having a torque of 250 pound feet and moving with a speed of 600 revolutions per minute is 28.56 hp.

Ques. Find the speed of the vehicle if the horsepower of it is 0.96 hp and has a torque of 200 pound feet. (3 Marks)

Ans. We have, the Torque=200 pound feet and Horsepower=0.96 hp

Using the Horsepower formula, we get

Speed of the vehicle=Horsepower5252Torque

Speed of the vehicle=0.965252200

Speed of the vehicle=25.2 rpm

Therefore, the speed of the vehicle if the horsepower of it is 0.96 hp and has a torque of 200 pound feet is 25.2 revolutions per minute.

Ques. Find the horsepower of a vehicle having a torque of 150 pound feet and moving with a speed of 600 revolutions per minute?(3 Marks)

Ans. We have, the Torque=150 pound feet and Speed=600 rpm

Using the Horsepower formula, we get

Horsepower of the vehicle=TorqueSpeed5252

Horsepower of the vehicle=6001505252

Horsepower of the vehicle=17.13 hp

Therefore, the horsepower of the vehicle having a torque of 150 pound feet and moving with a speed of 600 revolutions per minute is 17.13 hp.

Ques. Determine the horsepower of a vehicle which moves with a speed of 600 revolutions per minute and has a torque of 100 pound feet? (3 Marks)

Ans. We have, the Torque=100 pound feet and Speed=600 rpm

Using the Horsepower formula, we get

Horsepower of the vehicle=TorqueSpeed5252

Horsepower of the vehicle=6001005252

Horsepower of the vehicle=11.42 hp

Therefore, the horsepower of the vehicle having a torque of 100 pound feet and moving with a speed of 600 revolutions per minute is 11.4 2 hp.

Ques. How much Watt power makes one horsepower? (1 mark)

Ans. One horsepower equals 746 Watt, that is,

1 hp=746 W

Ques. Find the speed of the vehicle if the horsepower of it is 0.94 hp and has a torque of 250 pound feet. (3 Marks)

Ans. We have, the Torque=250 pound feet and Horsepower=0.94 hp

Using the Horsepower formula, we get

Speed of the vehicle=Horsepower5252Torque

Speed of the vehicle=0.945252250

Speed of the vehicle=19.7 rpm

Therefore, the speed of the vehicle if the horsepower of it is 0.94 hp and has a torque of 250 pound feet is 19.7 revolutions per minute.

Ques. What is the torque of a vehicle if it has a horsepower of 0.865 hp with a speed of 19 revolutions per minute? (3 Marks)

Ans. We have, the Speed=19 rpm and Horsepower=0.865 hp

Using the Horsepower formula, we get

Torque of the vehicle=Horsepower5252Speed

Torque of the vehicle=0.865525219

Torque of the vehicle=239.1 pound feet

Therefore, the torque of a vehicle having horsepower of 0.865 hp and a speed of 19 revolutions per minute is 239.1 pound feet.

Ques. What is the work done by a force of 30 N in lifting a load of 2 kg to a height of 10m? (Take g=10m/s2) (2 Marks)

Ans. We have, the Force=30N and Distance(Height)=10m

So, the formula for work done is given as,

Work done=ForceDistance

Work done=3010

Work done=300 J

Hence, the work done by a force of 30 N in lifting a load of 2 kg to a height of 10m is 300 J.

Ques. What is the torque of a vehicle if it has a horsepower of 12.4 hp with a speed of 500 revolutions per minute? (3 Marks)

Ans. We have, the Speed=500 rpm and Horsepower=12.4 hp

Using the Horsepower formula, we get

Torque of the vehicle=Horsepower5252Speed

Torque of the vehicle=12.45252500

Torque of the vehicle=130.24 pound feet

Therefore, the torque of a vehicle having horsepower of 12.4 hp and a speed of 500 revolutions per minute is 130.24 pound feet.

Also Read:

Value of g on Moon	Thermal properties of matter	Bernoulli’s principle
Stokes’ Law	Moment of inertia	Cyclic process
Heat engines	Celsius to Kelvin	Thermodynamic processes
Blackbody Radiation	Colorimeter	Difference between heat and temperature

Horsepower Formula: Definition, Calculation

What is meant by Horsepower (HP) ?

Horsepower Formula: Calculation

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

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Horsepower Formula: Definition, Calculation

What is meant by Horsepower (HP) ?

Horsepower Formula: Calculation

Things to Remember

Sample Questions

CBSE CLASS XII Related Questions

1. Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3. If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

4. If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Draw the number of scattered particles versus the scattering angle graph for scattering of alpha particles by a thin foil. Write two important conclusions that can be drawn from this plot.

2.
A tank is filled with a liquid to a height of \( 12.5 \, \text{m} \). The apparent depth of a needle lying at the bottom of the tank is measured to be \( 9.0 \, \text{m} \). Calculate the speed of light in the liquid.

3.
If Bohr’s quantization postulate (angular momentum \( = \frac{nh}{2\pi} \)) is a basic law of nature, it should be equally valid for the case of planetary motion also. Why, then, do we never speak of quantization of orbits of planets around the Sun? Explain.

4.
If both the number of protons and the neutrons are conserved in each nuclear reaction, in what way is mass converted into energy (or vice versa) in a nuclear reaction? Explain.

5.
Suppose a pure Si crystal has \( 5 \times 10^{28} \) atoms per \( \text{m}^3 \). It is doped with \( 5 \times 10^{22} \) atoms per \( \text{m}^3 \) of Arsenic. Calculate majority and minority carrier concentration in the doped silicon. (Given: \( n_i = 1.5 \times 10^{16} \, \text{m}^{-3} \))

6.
Draw a circuit diagram of a full-wave rectifier using p-n junction diodes. Explain its working and show the input-output waveforms.