Water is a crucial resource for our survival, and it is utilized in many industries, including the automobile industry. Water is often used to cool and lubricate the engine of a vehicle. However, the flow of water must be regulated to ensure that the engine does not experience any damages. This is where the concept of pipe diameter, pressure, and vertical distance comes into play.
In this case, we are presented with a scenario where water enters a motor through a 600 mm diameter pipe under a pressure of 14 KPa. The water then exits through a 900 mm diameter exhaust pipe with a pressure of 4 KPa. There is a vertical distance of 2.5 m separating the centers of the two pipes at the sections where the pressures are measured. We are also told that 500 liters of water pass the motor each second.
To calculate the power supplied to the motor, we need to use the formula:
Power (P) = Flow rate (Q) x Pressure difference (ΔP)
In this case, the flow rate is 500 L/s or 0.5 m³/s. The pressure difference is calculated as the difference between the inlet and outlet pressures, which is 14 KPa - 4 KPa = 10 KPa.
Therefore, the power supplied to the motor is:
P = 0.5 m³/s x 10,000 N/m² = 5000 Nm/s
However, this is just the theoretical power supplied to the motor. In reality, some of the energy is lost due to friction and other factors. This is accounted for by the motor's efficiency, which is defined as:
Efficiency = Output power / Input power
Output power refers to the power delivered to the motor, while input power refers to the power supplied to the system. In this case, we can assume that all the power supplied to the system goes into the motor since there is no other component in the system that would consume energy. Therefore, the input power is equal to 5000 Nm/s, and the efficiency is:
Efficiency = Pout / Pin = P / 5000 Nm/s = P/5 kW
We can rearrange this formula to calculate the output power:
Pout = Efficiency x Pin = Efficiency x 5 kW
For example, if the motor's efficiency is 90%, then the output power is:
Pout = 0.9 x 5 kW = 4.5 kW
In conclusion, the diameter of the pipe, pressure, and vertical distance play a critical role in regulating the flow of water and determining the power supplied to the motor. It's crucial to consider these factors to ensure that the engine runs smoothly and efficiently. By calculating the power supplied to the motor and the system's efficiency, we can optimize its performance and minimize energy losses.