Find velocity of air using Bernoulli principle

[goatz4real]

Homework Statement

A horizontal stream of air is blown just above the open end of the hares apparatus with an initial speed "V". The density of air is 1.2 kgm^-3.Then the water column rises to 6 cm in the respective limb.Density of water is 10³ kgm^-3
Using Bernoulli`s principle find "V"

Homework Equations

1/2 x ρ x V²= P₂ - P₁

The Attempt at a Solution

( 1/2 x 1.2 kgm^-3 x V² ) + ( 1.2 kgm^-3 x 10 ms^-2 x 6/100 m ) = 6/100 m x 10³ kgm^-3 x 10 ms^-2

V = √1000-1.2[/B]

*** This is the answer I got , but its wrong. Please help me out , I`ve tried this several times and I
keep getting the same answer

 

[Andrew Mason]

Homework Equations

1/2 x ρ x V²= P₂ - P₁

The Attempt at a Solution

( 1/2 x 1.2 kgm^-3 x V² ) + ( 1.2 kgm^-3 x 10 ms^-2 x 6/100 m ) = 6/100 m x 10³ kgm^-3 x 10 ms^-2

V = √1000-1.2[/B]

*** This is the answer I got , but its wrong. Please help me out , I`ve tried this several times and I
keep getting the same answer

Your equation is correct.

The decrease in pressure is the weight of the 6cm of water per m^3 (measured in Pascals or Newtons/m^2) less the weight of 6cm of air per m^3. You can probably ignore the weight of the air because it is so much less than the water.

Then it is just a matter of setting V = 2ΔP/ρ.

If your instructions do not state that g = 10 m/sec^2 I would suggest that you use 9.8 m/sec^2 and see if that gives you the correct answer. If not, try ignoring the weight of the air and just use the pressure of 6cm of water as the ΔP.

AM

 

[Buzz Bloom]

I confess I do not understand this problem. In particular I am confused that the diagrammed apparatus has two columns, one water and one oil, and that none of the discussion mentions the oil. Why is the oil irrelevant?

 

[Andrew Mason]

The oil is not relevant based on the information given. What matters is the pressure in the glass tube and in the beaker. The height of the fluid will adjust so that the pressure on the fluid under the tube is the same as the pressure at the same level in the beaker. Oil is less dense than water so the column of oil will be greater. Two columns are needed to show the Bernoulli effect. They could have used water in both but then they would have to distinguish between the left and right column.

Did you get the right answer?

AM

 

[Buzz Bloom]

Two columns are needed to show the Bernoulli effect. They could have used water in both but then they would have to distinguish between the left and right column.

Hi Andrew:

Thanks for responding to my question.

I still have some confusion. I get that two columns are needed, but I thought that the difference between the heights of the two columns was relevant. Perhaps that is my misunderstanding. If the height difference is relevant, then the difference between water and oil density would also be relevant, but that was not discussed.

Regards,
Buzz