Question

Suppose that you go to McDonalds and buy a chocolate milkshake. In order to drink the milkshake, you will have to raise the fluid 5 cm up through the straw to your mouth. You can do this by sealing your lips around the straw and expanding the volume of the trapped air inside your mouth. This will cause the air pressure inside the straw to drop below Atmospheric Pressure (as we discussed in class). If the density of the milkshake is 1110 kg/m³, by how many Pascals (Pa) must the air pressure inside your mouth be reduced below atmospheric pressure to drink the milkshake? The Earth's Atmospheric Pressure is 101.325 kPa.

Answer 1

Call the area of the straw A (you don't need to know what the area is, you would get the same answer no matter what size straw you used).

The volume of milkshake is the height * A = 5 cm * A

The mass of milkshake is density * volume = 1110 kg/m^3 * 5 cm * A

The force exerted by that mass = mass * acceleration due to gravity = 1110 kg/m^3 * 5 cm * A * a

Pressure = force / area = 1110 kg/m^3 * 5 cm * A * a / A, note how the A cancels out, that is why the size of the straw doesn't matter

Pressure = 1110 kg/m^3 * 5 cm * a = 1110 kg/m^3 * 5 cm * 9.82 m/s^2 (substituting for the acceleration due to gravity).

If we convert 5 cm to m, we cancel out a m term

Pressure = 1110 kg/m^3 * 0.05 m * 9.82 m/s^2

Pressure = 545.01 kg/ms^2

Pa has the units kg/ms^2, 1 Pa = 1 kg/ms^2 so the units on the right hand side is Pa

Pressure = 545.01 Pa