How does Bernoulli's equation relate to surface pressure on an isothermal plate?

[BMWPower06]

Surface Pressure Equation??

Homework Statement

Given pressure and the free stream velocity as well as the temperature of the isothermal plate.

Homework Equations

This is where I'm lost?

The Attempt at a Solution

It asks me to plot the surface pressure at the isothermal plate for a range of x=0 to x=1 given that I have a free stream velocity of 10*x

Can someone help me, I'm not sure what the equation is for surface pressure.

Thanks

 

[BMWPower06]

any help?

 

[SteamKing]

Have you tried Bernoulli's equation?

 

[BMWPower06]

Have you tried Bernoulli's equation?

are you referring to this equation?

 

[BMWPower06]

Do I just solve for P in the above equation and that will give me surface pressure? What constant value do I use?

 

[SteamKing]

The problem gives you a free stream velocity relationship using distance as the independent variable. What the problem wants you to show is how P must vary as v changes so that Bernoulli's equation is satisfied.

 

[BMWPower06]

The problem gives you a free stream velocity relationship using distance as the independent variable. What the problem wants you to show is how P must vary as v changes so that Bernoulli's equation is satisfied.

So do I solve for P/V=

Also, I'm still confused as to what the constant in the equation above represents?

Thanks

 

[BMWPower06]

So do I solve for P/V=

Also, I'm still confused as to what the constant in the equation above represents?

Thanks

any help?

 

[SteamKing]

The point of Bernoulli's equation is not to determine the numerical value of the constant. One uses the fact that a change in anyone of the quantities on the LHS of the equation (like the velocity of the fluid) will cause a change in the other quantities. For example, if the velocity of the stream increases and there is no change in elevation, then pressure must decrease, so that the constant, whatever it is, doesn't change.

 

[BMWPower06]

The point of Bernoulli's equation is not to determine the numerical value of the constant. One uses the fact that a change in anyone of the quantities on the LHS of the equation (like the velocity of the fluid) will cause a change in the other quantities. For example, if the velocity of the stream increases and there is no change in elevation, then pressure must decrease, so that the constant, whatever it is, doesn't change.

Ahh okay, so basically at x=0 the pressure is 300kPa. So to plot the change in surface pressure I would do the following:

300 - [(1/2)*rho*(Uinfinity^2) - (rho*g*x)]

Where Uinfinity is the free stream velocity.

Is that correct? Since I am given that the pressure a tthe surface plate is 300kPa?

Thanks for the help SteamKing!

 

[SteamKing]

I would rewrite Bernoulli's equation so that you had [v, z, p] @ loc. 1 = [v, z, p] @ loc. 2
Then it would be clear how P changes as v changes with location.