Not sure how to approach this problem. Seems simple. Here it is...
An airplane is moving through still air at 60m/s. At some point on the wing, the air pressure is -1200N/m^2 gauge. If the density of air is 0.8kg/m^3, find the velocity of the flow at this point. Carefully list the assumptions you have made in your analysis. Express your answer in terms of nondimensional pressure coefficient Cp.
I can tell you that Cp=(p-pinf)/qinf, where pinf is the free stream pressure and qinf=0.5*freestremdensity*freestreamvelociy^2.
Any help would be much appreciated...
To find the velocity of the flow at the specific point on the wing, we can use the pressure coefficient equation Cp = (p - pinf) / qinf, where Cp is the pressure coefficient, p is the pressure at that point on the wing, pinf is the free stream pressure, and qinf is the dynamic pressure.
First, we need to determine the dynamic pressure qinf. The dynamic pressure is given by the equation qinf = 0.5 * freestreamdensity * freestreamvelocity^2.
Given that the freestream air velocity is 60 m/s and the freestream air density is 0.8 kg/m^3, we can substitute these values to calculate qinf.
qinf = 0.5 * 0.8 kg/m^3 * (60 m/s)^2
= 1440 N/m^2
Next, we need to determine the pressure coefficient Cp using the given air pressure at that point on the wing. Cp = (p - pinf) / qinf, where p is the pressure at that point on the wing and pinf is the free stream pressure.
Given that the air pressure at that point on the wing is -1200 N/m^2 gauge, we can substitute these values to calculate Cp.
Cp = (-1200 N/m^2 - pinf) / 1440 N/m^2
Now, we can rearrange the equation to solve for the free stream pressure pinf.
pinf = -1200 N/m^2 - Cp * 1440 N/m^2
Finally, we can substitute the calculated pinf and qinf into the equation for Cp to calculate the velocity of the flow at that point on the wing.
Cp = (p - (-1200 N/m^2 - Cp * 1440 N/m^2)) / 1440 N/m^2
Simplifying the equation, we can solve for Cp.
1440 Cp = p + 1200 N/m^2 + 1440 Cp * 1440 N/m^2
1440 Cp - 1440 Cp * 1440 N/m^2 = p + 1200 N/m^2
1440 Cp(1 - 1440 N/m^2) = p + 1200 N/m^2
p = 1440 Cp(1 - 1440 N/m^2) - 1200 N/m^2
The velocity of the flow at that point on the wing can then be expressed in terms of the nondimensional pressure coefficient Cp.
Please note that this solution assumes incompressible flow and steady-state conditions. It also assumes that the air density remains constant throughout the flow.