Bernoulli's equation - finding the pressure at the top of a tube

In summary, The conversation discusses the problem of a horizontal tube connected to a vertical tube submerged in a liquid. Air is forced into the horizontal tube, causing a pressure difference that sucks the liquid up the vertical tube. The question is posed about the pressure at the top of the vertical tube and the answer is given as P = Po - 1/2 * /rhoA * v^2, derived from Bernoulli's equation. The individual conversing initially struggled to derive this equation, but eventually figured it out.
  • #1
Sigma Rho
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Here's my problem:-

A horizontal tube has a T-junction with a vertical tube coming downwards into a container of liquid, at height h below the T-junction. Air is forced into the horizontal tube which causes a pressure difference which sucks the liquid up the vertical tube.

What is the pressure at the top of the vertical tube?

I have the answer as
P = Po - 1/2 * /rhoA * v^2

where:
P = pressure at top of vertical tube
Po = atmospheric pressure
/rhoA = density of air in tube
v = velocity of air in tube

but I can't seem to derive this equation from Bernoulli's equation. (Or anything else! :confused: )

Any ideas?

Thanks.
 
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  • #2
s'okay, I've just worked it out. It was embarassingly simple!
 

FAQ: Bernoulli's equation - finding the pressure at the top of a tube

What is Bernoulli's equation and how is it used to find the pressure at the top of a tube?

Bernoulli's equation is a fundamental principle in fluid mechanics that describes the relationship between fluid velocity, pressure, and elevation. It states that as the velocity of a fluid increases, the pressure decreases. This equation can be used to calculate the pressure at the top of a tube by considering the fluid's velocity and elevation at that point.

What are the assumptions made in using Bernoulli's equation to find pressure at the top of a tube?

The assumptions made in using Bernoulli's equation include: 1) the fluid is incompressible, 2) the flow is steady and laminar, 3) the fluid is non-viscous, and 4) there is no energy loss due to friction or turbulence.

Can Bernoulli's equation be used for any type of fluid?

No, Bernoulli's equation is only applicable to incompressible fluids, such as water or air at low velocities. It cannot be used for compressible fluids, such as gases at high velocities, or for fluids with high viscosity.

What are the units for the variables in Bernoulli's equation?

The units for the variables in Bernoulli's equation are: velocity in meters per second (m/s), pressure in pascals (Pa), and elevation in meters (m).

What are some real-world applications of Bernoulli's equation for finding pressure at the top of a tube?

Bernoulli's equation has numerous applications in engineering and physics, including calculating the pressure at the top of a tube in water distribution systems, air ventilation systems, and airplane wings. It is also used in designing fluid pumps, turbines, and other hydraulic machinery.

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