A pressure gage connected to a tank reads 50 psi at a location where the barometric reading is 29.1 in Hg. Determine the absolute pressure in the tank. Take ρHg = 848.4 lbm/ft³.
Understand the Problem
The question is asking for the calculation of the absolute pressure in a tank based on given values: the pressure gauge reading, the barometric pressure, and the density of mercury. We need to use the appropriate formula to convert the given pressure to absolute pressure.
Answer
The absolute pressure is \( P_a = 64.32 \, \text{psi} \).
Answer for screen readers
The absolute pressure in the tank is ( P_a = 64.32 , \text{psi} ).
Steps to Solve
- Identify Given Values
From the problem, we have:
- Gauge pressure ( P_g = 50 , \text{psi} )
- Barometric pressure ( P_b = 29.1 , \text{in Hg} )
- Density of mercury ( \rho_{Hg} = 848.4 , \text{lbm/ft}^3 )
- Convert Barometric Pressure to psi
Using the conversion of inches of mercury to psi, we can convert the barometric pressure: [ 1 , \text{in Hg} = 0.4912 , \text{psi} ] Thus: [ P_b , \text{(in psi)} = 29.1 , \text{in Hg} \times 0.4912 , \frac{\text{psi}}{\text{in Hg}} = 14.32 , \text{psi} ]
- Calculate Absolute Pressure
The absolute pressure ( P_a ) can be calculated using the formula: [ P_a = P_g + P_b ] Substituting the values: [ P_a = 50 , \text{psi} + 14.32 , \text{psi} = 64.32 , \text{psi} ]
The absolute pressure in the tank is ( P_a = 64.32 , \text{psi} ).
More Information
Absolute pressure is the total pressure experienced by a fluid, including both the gauge pressure and the atmospheric pressure. In this problem, we added the gauge pressure from the tank to the atmospheric (barometric) pressure to find the absolute pressure.
Tips
- Misunderstanding the difference between gauge pressure and absolute pressure. Always remember that absolute pressure includes atmospheric pressure.
- Incorrectly converting units, such as failing to convert inches of mercury to psi properly.
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