Lift and Pressure Question ( )

In summary, lift is the upward force that allows an object to move through the air, created by a difference in air pressure caused by the shape and speed of the object. It is directly related to pressure, which is affected by factors such as the object's shape and size, speed, and the density of the air. Lift and pressure are crucial for flight, allowing an object to stay airborne and control its movement. They can be calculated and measured using equations and instruments such as pressure gauges and airspeed indicators.
  • #1
physicsCU
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I also posted this in the homework help, but I may get more help here.

This is the problem:

We are given either a local velocity or local coefficient of pressure. Using one, the other can be solved. Freestream V is given.

Now, if that Cp is the average Cp on the upper surface of a wing and that upper surface provides 3/4 of the lift, what is the coefficient of lift?

How would I solve the integrand of the cl integral?
 
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respond to the homework help thread. Please do not doublepost.
 
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To solve for the coefficient of lift (Cl), we first need to understand the relationship between lift and pressure. Lift is a force that is generated by the difference in pressure above and below an object, such as a wing. This difference in pressure is caused by the air flowing over and under the wing, creating a lift force. The coefficient of pressure (Cp) is a dimensionless quantity that represents the pressure at a specific point on the wing, compared to the freestream pressure.

To find the coefficient of lift, we can use the lift equation: Lift = 1/2 * density * velocity^2 * lift coefficient * wing area. Since we are given the freestream velocity and the average coefficient of pressure on the upper surface of the wing, we can solve for the lift coefficient by rearranging the lift equation.

First, we need to determine the lift force on the wing. We are told that the upper surface of the wing contributes 3/4 of the total lift, so we can calculate the lift on the upper surface by multiplying the total lift by 3/4. Let's call this value L_upper.

L_upper = (3/4) * 1/2 * density * velocity^2 * lift coefficient * wing area

Next, we can use the definition of Cp to relate it to the lift coefficient. Cp = (pressure - freestream pressure) / (1/2 * density * velocity^2). Rearranging this equation, we get lift coefficient = 2 * Cp + 1.

Now, we can substitute this into our original equation for L_upper and solve for the coefficient of lift.

L_upper = (3/4) * 1/2 * density * velocity^2 * (2 * Cp + 1) * wing area

Finally, we can rearrange this equation to solve for Cl.

Cl = L_upper / (1/2 * density * velocity^2 * wing area) = (3/4) * (2 * Cp + 1)

Therefore, the coefficient of lift is equal to 3/4 times the average coefficient of pressure on the upper surface, plus 3/4.

To solve the integrand of the cl integral, you will need to use the provided values for Cp and integrate over the entire upper surface of the wing. This will give you the average Cp on the upper surface, which you can
 

1. What is lift and how does it work?

Lift is the force that allows an object, such as an airplane, to move upwards through the air. It is created when the shape of the object, such as the wings of an airplane, causes air to flow faster over the top of the object than underneath it. This creates a difference in air pressure, resulting in lift.

2. How is lift related to pressure?

Lift is directly related to pressure, as it is the difference in air pressure above and below an object that creates lift. The faster air moves over the top of an object, the lower the pressure becomes, resulting in a higher pressure differential and more lift.

3. What factors affect lift and pressure?

The shape and size of an object, as well as its speed and the density of the surrounding air, all affect lift and pressure. The angle of the object, known as the angle of attack, also plays a role in determining the amount of lift and pressure generated.

4. How does lift and pressure impact flight?

Lift and pressure are crucial for flight, as they allow an object, such as an airplane, to stay in the air and control its movement. Without lift, an object would not be able to overcome the force of gravity and stay airborne. Changes in lift and pressure also allow for changes in altitude and direction during flight.

5. How is lift and pressure calculated and measured?

Lift and pressure are calculated and measured using equations and instruments such as a pressure gauge or an airspeed indicator. The specific equations and instruments used depend on the object and conditions being studied. In general, lift and pressure can be calculated by considering the shape and speed of the object and the density of the surrounding air.

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