Calculating Gauge Pressure Have I worked it correctly?

In summary, the conversation is about a simple gauge pressure question involving compressing pure water and calculating the required pressure in both N/m^2 and psi, as well as determining the height of a steel bar needed to exert this pressure.
  • #1
predentalgirl1
67
1
Simple Gauge Pressure Question

(a) Calculate the gauge pressure (it does not include atmosphereric P) required to compress pure water from 1.000 L to 989 mL. Give an answer in both N/m^2 and psi, lb/in^2.

(b) What height in meters and feet of a 1x1 cm^2 steel bar (density=7.86 g/cm^3) is required to exert the pressure found in part (a)?







3.Work and answers in the attached file.
 

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  • #2
Avoid multiple postings

Hi, you seem to have posted the same question three times in different forums. I had given you an answer yesterday. If you didn't find my answer helpful. you could have just said so and others would have come forward to help you. Here's what I'd written.

==========================================
a. Use the formula for bulk modulus. B = delta P/(delta v)/v. B for water is 2.2*10^9 N/m^2.

I hope the other answers will follow.
==========================================

Where are you getting stuck?

Oh, I see that you have enclosed your work. We'll see it as soon as it's clear for approval.
 
Last edited:
  • #3


(a) To calculate the gauge pressure required to compress pure water from 1.000 L to 989 mL, we can use the formula: P = F/A, where P is the pressure, F is the force, and A is the area.

First, we need to find the change in volume of the water, which is 1.000 L - 989 mL = 0.011 L. Since 1 L = 1000 cm^3, the change in volume is 11 cm^3.

Next, we need to calculate the force required to compress this volume of water. The density of water is 1 g/cm^3, so the mass of the water is 11 g. Using the formula F = mg, where m is the mass and g is the gravitational acceleration (9.8 m/s^2), we can find the force to be 107.8 N.

Finally, we need to calculate the area over which this force is applied. The area of a 1x1 cm^2 steel bar is 1 cm^2 = 0.0001 m^2. Therefore, the gauge pressure required to compress the water is:

P = F/A = 107.8 N / 0.0001 m^2 = 1078000 N/m^2

Converting to psi, we get:

P = 1078000 N/m^2 * 0.00014503773773 psi/N/m^2 = 156.2 psi

Converting to lb/in^2, we get:

P = 1078000 N/m^2 * 0.000204816133 lb/in^2/N/m^2 = 220.8 lb/in^2

Therefore, the gauge pressure required to compress pure water from 1.000 L to 989 mL is 1078000 N/m^2 or 156.2 psi or 220.8 lb/in^2.

(b) To find the height of the steel bar required to exert this pressure, we can use the formula: P = ρgh, where P is the pressure, ρ is the density, g is the gravitational acceleration, and h is the height.

Substituting the values from part (a), we get:

156.2 psi = 7.86 g/cm^3 * 9.8 m/s^2 * h
 

1. How do I calculate gauge pressure?

To calculate gauge pressure, you need to subtract the atmospheric pressure from the absolute pressure. The formula is: gauge pressure = absolute pressure - atmospheric pressure.

2. What is the difference between gauge pressure and absolute pressure?

Gauge pressure is the measurement of pressure relative to atmospheric pressure, while absolute pressure is the total pressure exerted by a substance, including atmospheric pressure. Gauge pressure is typically used for measuring pressure in closed systems, while absolute pressure is used for open systems.

3. How do I know if I have calculated gauge pressure correctly?

To ensure that you have calculated gauge pressure correctly, you can compare your result to the expected value or use a pressure gauge to verify the accuracy of your calculation. You can also double-check your calculations and units to make sure they are correct.

4. Can I use any unit for gauge pressure?

No, gauge pressure should be measured in units of pressure, such as pounds per square inch (psi) or pascals (Pa). It is important to use the correct unit for your calculation to ensure accuracy.

5. How does temperature affect gauge pressure?

Temperature can affect gauge pressure if the substance being measured is a gas. As temperature increases, the molecules in the gas move faster, resulting in an increase in pressure. This is known as thermal expansion. It is important to take temperature into account when calculating gauge pressure to ensure accurate measurements.

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