Calculating Gauge Pressure at the Bottom of a Test Tube

In summary, the question asks for the gauge pressure on the bottom of a test tube containing 3.8 cm of oil with a density of 0.81 g/cm3 and 6.4 cm of water. The solution involves calculating the difference between the pressure at the bottom of the tube and atmospheric pressure, using the equations P1-Po = ρgh1 + ρgh2 and P1 = P2 + ρgh2. The final answer is 929 Pa.
  • #1
DrMcDreamy
68
0

Homework Statement



A test tube standing vertically in a test tube rack contains 3.8 cm of oil, whose density is 0.81 g/cm3 and 6.4 cm of water. What is the gauge pressure on the bottom of the tube? The acceleration of gravity is 9.8 m/s2. Answer in units of Pa

Homework Equations



P1-Po=[tex]\rho[/tex]oilgh1+[tex]\rho[/tex]H2Ogh2

The Attempt at a Solution



P1-Po= (810 kg/m3)(9.80 kg m /s2)(0.038 m) + (1000 kg/m3)(9.80 kg m/s2)(0.064 m)

P1-Po= 929 Pa

Is the work and answer right? TIA
 
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  • #2
They are indeed correct.
 
  • #3
Thank you! :smile:
 
  • #4
Actually, I wonder whether you should also consider atmospheric pressure.

Also, why is it P1-P0 and not +?
 
  • #5
^It came out right with 929 Pa.
The way the prof had shown it in class is P1-P0:

P2=Po+[tex]\rho[/tex]oilgh1

P1=P2+[tex]\rho[/tex]H2Ogh2

P1=Po+[tex]\rho[/tex]gh1+[tex]\rho[/tex]gh2

P1-Po=[tex]\rho[/tex]gh1+[tex]\rho[/tex]gh2
 
  • #6
Oh ok, it was down to notation, then.
When I thought you might need the atmospheric pressure is because I was calculating P1, but you needed P1-P0. :)
 

What is gauge pressure at the bottom?

Gauge pressure at the bottom refers to the amount of pressure exerted at the bottom of a container or vessel, measured relative to atmospheric pressure. It is commonly used in fluid mechanics to understand the pressure at different depths in a liquid or gas.

How is gauge pressure at the bottom calculated?

Gauge pressure at the bottom is calculated by subtracting the atmospheric pressure from the total pressure at the bottom of a container. This can be done using a pressure gauge or by using the formula P = ρgh, where P is pressure, ρ is density, g is acceleration due to gravity, and h is the depth of the liquid or gas.

What is the difference between gauge pressure and absolute pressure?

Gauge pressure is the pressure measured relative to atmospheric pressure, while absolute pressure is the total pressure at a given point, including atmospheric pressure. This means that absolute pressure will always be higher than gauge pressure.

Why is gauge pressure at the bottom important in fluid mechanics?

Gauge pressure at the bottom is important in fluid mechanics because it helps us understand how pressure changes with depth in a liquid or gas. This information is crucial in designing and analyzing systems that involve fluids, such as pipes, pumps, and tanks.

How does gauge pressure at the bottom affect the behavior of fluids?

Gauge pressure at the bottom affects the behavior of fluids by exerting a force on the fluid particles, causing them to move and flow. The pressure at the bottom also determines the direction and speed of fluid flow, as fluids always move from areas of high pressure to low pressure.

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