Homework SourseI need help with this riding lawn mower problem Give the ope
I need help with this riding lawn mower problem. Give the operating temperatures and efficiency, compute the work per cycle of the gasoline enginer and determine the amount of gasoline, in gallons, required to operate the gas mower for 2.8 hours. You can assume that all energy liberated in burning the fuel goes into Qh and that gasoline has an energy density of 46.4 MJ/kg.
| Ariens 42 in 17hp riding mower spec | Value |
| Mass with rider | 260kg |
| Rear wheel radius | 20cm |
| Gas engine power | 17hp |
| Gas engine max temp | 877k |
| Ambient temp | 293k |
| Gas engine efficiency | 0.5 of Carnot |
| Gas engine RPM | 1500RPM |
| Two cutting DC motors, power, each | 500W |
| Cutter blade RPM | 1000RPM |
| Cutter blade radius | 20cm |
| Runtime requirement, hours | 2.8hours |
| 1.440 kWh battery mass | 27kg |
| Max speed required | 3m/s |
| Estimated coefficient of friction while mowing | 0.1 |
Solution
Power Required to operate the mower = friction coefficient * weight * velocity
= 0.1 * (260 + 27) * 9.8 * 3 = 843.78 W
Power Required to operate the cutting motor = 2 * 500 = 1000 W
Total power required = 1843.78 W
Efficiency of gas engine = 0.5 * ( 1 - 293 / 877) = 33.3 %
power input to engine = 1843.78 / efficiency = 5537.6543 W
mass of gasoline * 46400000 = 5537.6543 * 2.8 * 3600
mass of gasoline = 1.203 kg
volume of gasoline = 1.203 / 719.7 = 0.0016715 m^3 or 0.44156 gallons
