Solving Review Questions for Test: Bernoulli's Principle, Buoyancy, and More

[Haftred]

I need some help with some review questions for the test. I am trying to check the answers I get with the ones the teacher provided, bit I'm getting stuck. Knowing which equations to use etc... would be really helpful.

What is the maximum weight an aircraft with a wing area of x m^2 can lift if the air passing beneath the wing moves at y m/s and the air above the wing moves at z m/s?

Bernoulli's principle I know, but I don't know how to relate it to the wing area.

A barge with a horizontal cross-sectional area of x m^2 at the water line carries oil with a density z, which is less than that of water. When the oil is loaded the ship goes up y meters. How much oil was delivered?

I set buoyant force = mg but got stuck

Suppose a person can reduce the pressure in their lungs to x mmHG below atmospheric pressure. What is the maximum height that water can be drawn up a straw?

Just need to know how to do these problems. Any help appreciated.

 

[Gokul43201]

1. From the flow velocities, you can find the net upward pressure on the wing (Bernoulli). Multiplying by the area gives the net upward force on each wing.

2. The product of the cross section and the height tells you the change in the volume of water displaced. Recall the relation (Archimedis) between the density and the volume of water displaced.

3. Draw a diagram showing a glass of water, the straw with water rising up to some height, h, and the pressures acting at all relevant positions. It's not too hard once you do that.

 

[wais]

For the first question, you can use Bernoulli's principle to calculate the maximum weight the aircraft can lift. The equation for Bernoulli's principle is P1 + (1/2)ρv1^2 + ρgh1 = P2 + (1/2)ρv2^2 + ρgh2, where P is pressure, ρ is density, v is velocity, and h is height. In this case, the air passing beneath the wing has a higher velocity (y m/s) compared to the air above the wing (z m/s). This results in a difference in pressure between the two areas. By rearranging the equation, you can solve for the pressure difference, which can then be used to calculate the maximum weight the wing can lift.

For the second question, you can use the buoyant force equation, which is Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the object submerged, and g is the acceleration due to gravity. In this case, the buoyant force must be equal to the weight of the barge plus the weight of the oil cargo. By setting the buoyant force equal to the total weight, you can solve for the volume of oil delivered.

For the third question, you can use the equation P1V1 = P2V2, where P is pressure and V is volume. In this case, the person is able to reduce the pressure in their lungs by x mmHG, which means the pressure in their lungs is lower than the atmospheric pressure. By setting the two pressures equal to each other, you can solve for the maximum height that water can be drawn up a straw.

Remember to always pay attention to the units and conversions when doing these types of problems. Also, make sure to use the correct equations and substitute the given values into the equations. If you are still having trouble, it may be helpful to review the concepts and equations from your class notes or textbook. Good luck with your test!