What is the gauge pressure at point B?
The gauge pressure at point B is 22 kPa.
Calculation:
Given gauge pressure at point A is 50 kPa, diameter is 3.0 cm, speed is 2.0 m/s, and the gauge pressure at point B is 22 kPa.
Understanding Gauge Pressure:
Gauge pressure (Pg) is the pressure measured with respect to atmospheric pressure. It is the pressure indicated by a pressure gauge and does not include atmospheric pressure. In other words, gauge pressure is the pressure above atmospheric pressure.
Calculating Gauge Pressure:
To calculate gauge pressure, you need to subtract the atmospheric pressure from the absolute pressure. The formula for gauge pressure (Pg) is:
Pg = P - Patm
Where:
- Pg = Gauge pressure
- P = Absolute pressure
- Patm = Atmospheric pressure
Example:
If the absolute pressure is 100 kPa and the atmospheric pressure is 10 kPa, then the gauge pressure would be:
Pg = 100 kPa - 10 kPa
Pg = 90 kPa
Gauge Pressure at Point B:
In the given scenario, the gauge pressure at point B is 22 kPa. This means that the pressure at point B is 22 kPa higher than the atmospheric pressure in that location.
In conclusion, gauge pressure is an essential concept in fluid mechanics that helps in understanding the pressure at a certain point relative to atmospheric pressure. Calculating gauge pressure involves subtracting atmospheric pressure from absolute pressure. In the context of the water line example, knowing the gauge pressure at different points helps in determining the flow characteristics and pressure distribution within the pipe system.