A utube manometer contains mercury of density 13,600 kg/m3. One end of the manometer is open to the atmosphere and the other end is connected to a low pressure natural gas line. A height difference of 11.8 cm results between the levels of the two liquid columns, with the side connected to the game line being lower. The atmospheric pressure is 99,200 Pa.
1. What is the absolute pressure inside the gas line in pascals?
2. What is the gauge pressure in psi units?
would I apply bernailli's equation here? i know the density is higher in this so does that mean the pressure will be higher? i'm confused...
To solve this problem, you don't need to apply Bernoulli's equation. You can use the concept of hydrostatic pressure to find the absolute pressure inside the gas line and then convert it to gauge pressure.
Here's how you can find the answers to the questions:
1. Absolute pressure inside the gas line in pascals (Pa):
First, you need to determine the pressure due to the height difference of the mercury columns. The hydrostatic pressure is given by the formula:
Pressure = density * gravity * height
Since both sides of the manometer are open to the atmosphere, the pressure difference is equal to the difference in the mercury column heights. The height difference is given as 11.8 cm, which is equal to 0.118 m.
Therefore, the pressure difference is:
Pressure difference = density * gravity * height difference
= 13600 kg/m3 * 9.8 m/s2 * 0.118 m
Now, to find the absolute pressure inside the gas line, you need to add the pressure difference to the atmospheric pressure:
Absolute pressure = atmospheric pressure + pressure difference
= 99200 Pa + (13600 kg/m3 * 9.8 m/s2 * 0.118 m)
2. Gauge pressure in psi units:
Gauge pressure is the difference between the absolute pressure and atmospheric pressure. To convert the absolute pressure in pascals to psi (pounds per square inch), you can use the conversion factor:
1 psi = 6894.76 Pa
So, to convert the absolute pressure from pascals to psi units, use the following formula:
Gauge pressure (psi) = (Absolute pressure - atmospheric pressure) / 6894.76
Now, plug in the values you obtained for the absolute pressure and atmospheric pressure to calculate the gauge pressure in psi.
Note: Make sure to use consistent units in your calculations for accurate results.
By following these steps, you can find the answers to the given questions.