# Brake Horsepower

on . Posted in Fluid Dynamics

Brake horsepower, abbreviated as BPH, is a unit of power measurement for engines that represents the amount of power an engine produces without any external factors affecting the performance, such as the loss of power due to friction or other components.  It is a measure of the engine's raw power output.

The term "brake" in brake horsepower comes from the early days of engine testing when a brake was used to load the engine and measure its power output.  The brake horsepower is calculated by measuring the torque produced by the engine and multiplying it by the angular velocity (rotational speed) of the engine's output shaft.  Mathematically, brake horsepower (BHP) can be expressed as:

Brake horsepower is used to compare the power output of different engines or to evaluate the performance of a specific engine under controlled conditions.  It's worth noting that the actual power delivered to the wheels of a vehicle, known as wheel horsepower, will be less than the brake horsepower due to various losses in the drivetrain and other components.

### Brake Horsepower formula

$$BHP = Q \; h_t \; SG \;/\; 3960 \; \eta$$     (Brake Horsepower)

$$Q = BHP \; 3960 \; \eta \;/\; h_t \; SG$$

$$h_t = BHP \; 3960 \; \eta \;/\; Q \; SG$$

$$SG = BHP \; 3960 \; \eta \;/\; Q \; h_t$$

$$\eta = 3960 \; BHP \;/\; Q \; h_t \; SG$$

Symbol English Metric
$$BHP$$ = brake horsepower $$lbf-ft\;/\;sec$$ $$Btu\;/\;s$$
$$Q$$ = flow rate $$ft^3\;/\;sec$$ $$m^3\;/\;s$$
$$\eta$$  (Greek symbo; eta) = efficiency $$dimensionless$$
$$h_t$$ = total head $$ft$$ $$m$$
$$SG$$ = specific gravity $$dimensionless$$

### Brake Horsepower formula

$$1 \; HP = 5252\; RPM$$   When charting torque and horsepower, the math always cross at 5252 RPM.

$$BHP = \tau \; RPM \;/\; 5252$$     (Brake Horsepower)

$$\tau = BPH \; 5252 \;/\; RPM$$

$$RPM = BPH \; 5252 \;/\; \tau$$

Symbol English Metric
$$BHP$$ = brake horsepower $$lbf-ft\;/\;sec$$ $$Btu\;/\;s$$
$$\tau$$  (Greek symbol tau) = engine torque $$lbf-ft$$ $$N-m$$
$$RPM$$ = revolution per minute $$rev\;/\;min$$ $$rev\;/\;m$$

Tags: Horsepower