Fluid Mechanics: Pressure in Fluids

In summary: In that case, the oil in the connecting tubes has a much greater density than the gas, so the mercury level in the venturi meter will be much higher than when the venturi meter is used for a gas with negligible density.In summary, the oil in the connecting tubes has a much greater density than the gas, so the mercury level in the venturi meter will be much higher than when the venturi meter is used for a gas with negligible density.
  • #1
Lukas_RSA
6
0

Homework Statement


The gauge pressure at the inlet of a horizontal venturi meter is 40kPa. The vacuum at the throat is 38 mm mercury. If a differential U-tube manometer containing mercury is the U-tube and the oil in the connecting tubes is connected to the venturi, what will the difference in the mercury levels be? the fluid in the venturi meter is oil with a relative density of 0.8. Answer [0,359m]

The Attempt at a Solution



I have no idea how to start with this problem, i am assuming to use the following formulas but i don't understand them,

P1 - P1 / (p_oil)(g) = (S_m - 1) h_m

but i don't know how to get the answer, please assist me with this, i am going to youtube now to look for some tutorials on the u-tube manometer, you can also refer me to a great tutorial :-)

upload_2015-10-26_7-14-35.png
 
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  • #2
What do you do when you want to compare two quantities with the same dimension but expressed in different units ?
 
  • #3
hi BvU

thanks for you response sorry for taking so long to respond but i am busy studying so my time on the pc is a bit limited :-)

i am trying to convert the 38mm of mercury to a pressure so that i can then use the conservation method, put one side equal to the other side, then try to determine the height of the difference in mercury, but when i use P2=pgh and substitute the 38 mm in h i don't get the answer i am looking for, is this approach even the right approach?
after the P2=pgh

i put P1 = P2+ p(mercury)gh(x value)

40 000 = (-5068) + 133416x
40 000 + 5068 / 133416 = x
x = 0.3378m

the textbook says the answer should be 0.359m, is my logic wrong?

i hope to hear from you soon.

regards
Lukas van Rooyen
 
  • #4
Hello Lukas,

Several remarks:
Apparently you do everything in terms of gauge pressure. I'm a physicist and find it infinitely safer to work with actual (absolute) pressures. Never mind.

Your ##-##5068 is ##\rho\,g\,h## (but 38 mm * 13690 kg/m3 * 9.81 m/s2 = 5100 kg m/s2.!?) . [edit] my mistake -- ##\rho## is smaller

What they mean when they say the vacuum is 38 mm is a mystery to me. Perhaps they indeed mean the gauge pressure is ##-##38 mm (you'll have to get that out of the context of your book I suppose), in which case I can understand your calculation (but I get 335.8 mm).
But that's assuming the whole story
If a differential U-tube manometer containing mercury is the U-tube and the oil in the connecting tubes is connected to the venturi, what will the difference in the mercury levels be? the fluid in the venturi meter is oil with a relative density of 0.8.
doesn't change a thing. But it does ! -- if you make one assumption about this venturi meter: that it's used for a gas with negligible density.
 
Last edited:

Related to Fluid Mechanics: Pressure in Fluids

1. What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids (liquids and gases) in motion and at rest. It involves the application of equations and principles to understand the behavior of fluids and the forces acting upon them.

2. What is pressure in fluids?

Pressure in fluids is the force exerted by the fluid on its container or any surface in contact with it. It is a measure of how much force is distributed over a certain area. The SI unit of pressure is Pascal (Pa) and it is expressed as force per unit area.

3. How is pressure in fluids calculated?

Pressure in fluids is calculated using the equation P = F/A, where P is the pressure, F is the force applied, and A is the area of the surface on which the force is applied. This equation is based on the principle that pressure is directly proportional to force and inversely proportional to area.

4. What factors affect pressure in fluids?

The factors that affect pressure in fluids include the density of the fluid, the depth of the fluid, and the acceleration due to gravity. The pressure also varies with the shape of the container, as well as the fluid's temperature and state (liquid or gas).

5. What are some real-life applications of pressure in fluids?

Pressure in fluids has many practical applications, such as in hydraulic systems, where it is used to transfer and amplify forces. It is also important in weather systems, as changes in air pressure can indicate upcoming weather patterns. Additionally, understanding pressure in fluids is crucial in designing and operating aircraft, ships, and submarines.

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