How Fast Must Air Travel to Draw Water Up a Straw?

[Nellen2222]

Homework Statement

On a bet, you try to remove water from a glass by blowing across the top of a vertical straw immersed in the water
What is the minimum speed you must give the air at the top of the straw to draw water upward through a height of 2.0cm?

Homework Equations

Bernoulli's eq. p1+1/2pv1^2+ pgh1 = p2+1/2pv22 + pgh2

The Attempt at a Solution

Tried to rearrange for velocity, I guess I did it wrong.

v= √2gh*rho2/rho1

( The square root should be a whole root, of like all the terms, not sure how do fix that part)

Did i rerarrange it wrong?Umm . I got 17.5, and 49 (somehow) , maybe I am pllugging things in right, but I am not sure what the right answer is , 17.5 isn't for sure.

 

[voko]

You need to consider two equations. One for water, another for air in the straw. The water equation has no speed, just the height difference. The air equation has no speed in the straw, and there is no height difference.

 

[Nellen2222]

So I have to have two separate bernoulli equations? I still don't get it.

 

[voko]

You have two fluids. So you have two equations.

 

[Nellen2222]

Solving for the velocity of both then subtracting..?

 

[Nellen2222]

p1+1/2pv1^2+ pgh1 = p2+1/2pv22 + pgh2

I don't get what I am using both fluids for.. I don't have velocities so I don't use them right?

I don't get how to encorporte athis into the eq? so this means i have two velocities but i am not given any variable for either so how i can solve for two variables..

p1+1/2pv1^2+ pgh1 = p2+1/2pv22 + pgh2

I don't see any relation except if i get rid of velocities and just do 1/2p + pgh1 = 1/2p + ph2 . But i have all of those values.. Unless i solve for pressure by doing P= p(atmosphereic) + pgh, then i can get the pressure of the water in the straw

 

[voko]

Start with the equation for the air in the straw. What is the velocity just below the edge?

 

[Nellen2222]

It is 17.5 i think. I applied this formula v= √2gh*rho2/rho1

 

[voko]

How can the velocity in the straw be non-zero?

 

[Nellen2222]

air moves thru a straw wouldn't that make it non zero

 

[voko]

If air moves through the straw then the straw can't lift any water - it will have bubbles of air come through the water instead. You are supposed to move the air parallel to the edge.

 

[Nellen2222]

ok so V in the straw is 0..now what? :/ I really don't get it and this question is taking like hours..

 

[voko]

Now there is one equation for air. On one side, air is just above the edge. On the other it is just below. What is the difference in pressure?

 

[Nellen2222]

So I woud use the same formula for the bottom, and calculate the top.. and divide the bottom by the top? Or subtract the two values?

 

[voko]

I do not understand what you are saying.

 

[Nellen2222]

So I have one equation for air in the straw, Now i want another equation for water. Do I divide the eq for water by te one of straw? or plug in the values on the LS for air and the RS for water and solve for v1?

 

[voko]

You are going too fast. Answer my question in #13 first.

 

[rcgldr]

Blowing the air implies creation of a flow by increasing the static pressure of the blown air, which ideally remains higher than ambient until it's velocity goes to zero. The problem would be better stated that a vacuum is sucking air across the top of a straw, reducing the air's pressure and increasing it's speed.

Another detail being ignored here is that a vortice is created by air flowing over the exposed end of a straw, resulting in a futher reduction in pressure at the end of the straw. This could be elminated by having the end of the straw flush mounted to a flat plate perpendicular to the straw, so that the plate and straw act as a static port, where the pressure at the opening is the same as the static pressure of the air flowing across the port. I'm pointing this out in case someone decides to actually do an experiment with air blowing over the open end of a straw.

 

[szynkasz]

Calculate pressure needed to lift water by 2 cm. Air pressure must drop by that value due to its velocity.

 

[Nellen2222]

really? Can someone help me solve this. its been like 7 hours.

 

[Nellen2222]

Calculate pressure needed to lift water by 2 cm. Air pressure must drop by that value due to its velocity.

How do i calc. the pressure? Delta P?

 

[szynkasz]

Use Bernoulli equation for straw filled with water and for moving air.

 

[rcgldr]

How do i calc. the pressure? Delta P?

You have Bernoulli's equation for total pressure:

p1 + 1/2 ρ v1² + ρ g h1 = p2 + 1/2 ρ v2² + ρ g h2

Note that ρ is density. You'll need one Bernoulli's equation for the water, and another for the air, then you need to figure out how to combine the information from the two Bernoulli's equations. Hint, the water isn't moving, but it's height in the straw is 2 cm. The air is moving, and you can assume it's total pressure is ambient by assuming a vacuum is drawing air across the top of the straw, so that increased velocity corresponds to reduced pressure in accordance with Bernoulli's equation. Note the pressure of the water at the surface of the water outside the straw is the same as the pressure of ambient (not moving) air, and the pressure at the surface of the water inside the straw is the same as the static pressure of the air inside the straw. You can ignore the ρ g h term for the air, (the straw's height isn't given, and even if it was, ρ g h for the air would be nearly zero).