Question

Some car driving 60 mph on the highway uses 8 L of fuel per hour. The heating value HV of the fuel is about 42.4 MJ/kg and the density is 750 kg/m3 . If the thermal efficiency of the engine is 25%, then what is the power available at the crankshaft axis in bhp

Answer 1

The value is
`bhp = 24 \ hp`

Step-by-step explanation:

From the question we are told that

The velocity of the car is
`v = 60 \ mph`

Th amount of fuel used in an hour is
`a = 8 \ L = 8.0 *10^(-3) \ m^2/hr = (8.0 *10^(-3))/(3600) = 2.22 *10^(-6) \ m^3 /s`

The heating value of the fuel is
`HV =42.4 MJ/kg = 42.4 *10^(6) J/kg`

The thermal efficiency of the engine is
`\eta = 25\%=0.25`

Generally the rate at which the fuel is consumed is mathematically represented as

`\r Q = \rho * a`

Here
`\rho` is the density of fuel with value
`\rho = 750 \ kg /m^3`

`\r Q = 750 * 2.22*10^(-6)`

=>
`\r Q = 1.667 *10^(-3) \ kg /s`

Generally the power available at the crankshaft axis is mathematically represented as

`\r H_v = H_v * \r Q`

=>
`\r H_v = 42.4 *10^(6) * 1.667*10^(-3)`

=>
`\r H_v = 70668.08 \ W`

Converting to horse power

`\r H_v = ( 70668.08)/(735)`

=>
`\r H_v = 96.15 \ hp`

Generally the power available in the crankshaft in break hoarse power is mathematically evaluated as

=>
`bhp = 96.15 * \eta`

=>
`bhp = 96.15 * 0.25`

=>
`bhp = 24 \ hp`