Question

A car engine with a power output of 110 hp has a thermal efficiency of 28 percent. Determine the rate of fuel consumption if the heating value of the fuel is 19,000 Btu/lbm.

Short answer

Answer: The rate of fuel consumption for the car engine is approximately 52.62 lbm/hour.

Step-by-step solution

Convert power output to consistent units

In this problem, we are given the power output in horsepower (hp) which needs to be converted to BTU/hour, a unit that is consistent with the heating value of the fuel. The conversion factor is: 1 hp = 2545 BTU/hour. So, the power output of the car engine in BTU/hour is: 110 hp * 2545 BTU/hour/hp = 279,950 BTU/hour.

Calculate the energy provided by the engine

We are given the thermal efficiency of the engine as 28%. Thermal efficiency (η) is the ratio of the work output of the system to the heat input to the system. In this case, the work output is the power output of the engine. We can use the following formula to calculate the energy provided by the engine: Energy_input = Power_output / η where, Energy_input = Energy provided by the engine (BTU/hour) Power_output = 279,950 BTU/hour (from Step 1) η = 0.28 Energy_input = 279,950 BTU/hour / 0.28 = 999,821.43 BTU/hour

Calculate the rate of fuel consumption

We have found the energy provided by the engine (Energy_input) and we know the heating value of the fuel (19,000 BTU/lbm). We can now calculate the rate of fuel consumption by dividing the energy input by the heating value of the fuel: Rate_of_fuel_consumption = Energy_input / Heating_value_of_fuel where, Rate_of_fuel_consumption = rate of fuel consumption (lbm/hour) Energy_input = 999,821.43 BTU/hour (from Step 2) Heating_value_of_fuel = 19,000 BTU/lbm Rate_of_fuel_consumption = 999,821.43 BTU/hour / 19,000 BTU/lbm = 52.62 lbm/hour Thus, the rate of fuel consumption is approximately 52.62 lbm/hour.