# Fluids-blow across top of straw to draw up olive oil

• ryann_117
In summary, the question is asking for the minimum speed of air needed at the top of a straw immersed in olive oil to draw the oil upward through a height of 1.5 cm. The equation P1 + .5*density*v1^2 + density*g*y1 = P2 + .5*density*v2^2 + density*g*y2 can be used to solve for this minimum speed, with P1 representing the pressure at the bottom of the straw and P2 representing the pressure at the top. The calculation involves finding the pressure difference between the top and bottom of the straw and solving for v2, which is estimated to be 14.83 m/s.
ryann_117

## Homework Statement

You try to remove olive oil from a glass by blowing across the top of a vertical straw immersed in the olive oil. What is the minimum speed you must give the air at the top of the straw to draw olive oil upward through a height of 1.5 cm?
(Note: The density of olive oil, if you need it is 920 kg per cubic meter.)

## Homework Equations

P1 + .5*density*v1^2 + density*g*y1 = P2 + .5*density*v2^2 + density*g*y2

## The Attempt at a Solution

P1 + .5*density*v1^2 + density*g*y1 = P2 + .5*density*v2^2 + density*g*y2
P1 = .5*density*v2^2 + density*g*y2
V2 = 14.83 m/s
V2 is close, but not right; I'm not sure how to find P2. What do I need to do different?

I don't understand your calculations. How did you get from P1 = .5*density*v2^2 + density*g*y2 to v2=14.83 m/s?

You can calculate the pressure difference between the top and bottom of the straw that's needed to support the olive oil column; it's just rho*g*h. Then, you can apply the equation P1 + .5*density*v1^2 + density*g*y1 = P2 + .5*density*v2^2 + density*g*y2 with the left side representing the bottom of the straw and the right side representing the top. v1 would be 0, since the air at the bottom isn't moving, and you've just calculated P1-P2.

To determine the minimum speed required for the air at the top of the straw to draw up olive oil, we can use the Bernoulli's equation. This equation relates the pressure, density, and velocity of a fluid at two different points in a fluid flow. In this case, the two points are the top and bottom of the straw, where the fluid (air) is in motion.

Using the given information, we can set up the Bernoulli's equation as follows:

P1 + 0.5*density*v1^2 + density*g*y1 = P2 + 0.5*density*v2^2 + density*g*y2

Where P1 is the pressure at the top of the straw, P2 is the pressure at the bottom of the straw, v1 and v2 are the velocities at the top and bottom of the straw respectively, y1 and y2 are the heights at the top and bottom of the straw respectively, and g is the acceleration due to gravity.

Since we are trying to find the minimum speed, we can assume that the pressure at the top and bottom of the straw are equal (P1 = P2). This means that the pressure terms cancel out from the equation.

0.5*density*v1^2 + density*g*y1 = 0.5*density*v2^2 + density*g*y2

We are given the density of olive oil (920 kg/m^3) and the height through which the oil needs to be drawn (1.5 cm = 0.015 m). We can also assume that the velocity at the bottom of the straw is zero (v2 = 0) since the olive oil is at rest at the bottom.

Substituting these values into the equation, we get:

0.5*density*v1^2 + density*g*y1 = 0.5*density*0^2 + density*g*0.015

Solving for v1, we get:

v1 = √(2*g*y1)

Plugging in the values, we get:

v1 = √(2*9.8 m/s^2 * 0.015 m) = 0.39 m/s

Therefore, the minimum speed required for the air at the top of the straw to draw up olive oil through a height of 1.5 cm is 0.39 m/s.

## 1. How does blowing across the top of a straw draw up olive oil?

Blowing across the top of a straw creates a low-pressure area above the liquid, causing the air pressure inside the straw to decrease. This decrease in pressure allows the higher air pressure outside the straw to push the olive oil up and into the straw.

## 2. What type of fluid is olive oil?

Olive oil is a non-Newtonian fluid, meaning its viscosity changes depending on the force applied to it. It has a higher viscosity when it is stationary, but it becomes less viscous when a force, such as blowing air, is applied to it.

## 3. Will the amount of olive oil drawn up by the straw change if I blow harder?

Yes, the amount of olive oil drawn up by the straw will vary depending on the force of the air you blow. The harder you blow, the stronger the decrease in air pressure will be, and the more olive oil will be drawn up into the straw.

## 4. Why does the olive oil stop moving up the straw once it reaches a certain point?

The olive oil stops moving up the straw because it has reached equilibrium. The pressure inside the straw is now equal to the pressure outside, so there is no longer a pressure difference to push the oil up the straw.

## 5. Can I use this method to move other types of fluids?

Yes, this method can be used to draw up other types of fluids as long as they are not too viscous. The key is to create a pressure difference between the inside and outside of the straw, so it will work with any fluid that is affected by air pressure.

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