Using Bernoulli's Equation to find pressure in a wind tunnel

[Tanner Ross]

Homework Statement

A wind tunnel is designed to draw in air from the atmosphere and produce a velocity of 100m/s in the test section. THe fan is located downstream of the test section. What pressure is to be expected in the test section if the atmospheric temperature and pressure are -20C, 90kPa?

Homework Equations

Bernoulli's Equation: P₁ + 1/2pv² + pgh₁ = P₂ + 1/2pv² + pgh₂

p = P/RT

The Attempt at a Solution

I canceled out the heights as it doesn't state a height difference and says the fan is downstream, so assumed its a two dimensional problem. Leaving me with:

P₁ + 1/2pv² = P₂ + 1/2pv²

Then I used p = P/RT to find the density of air, which came out to be 1.24kg/m³

Then Isolated P₂ = P₁ - 1/2pv², using atmospheric pressure for P₁, I solved for the pressure afterwards but it came out to be -560kPa.

Now i know taking the absolute value is acceptable with pressures but this number still seems wrong to me.

 

[Tanner Ross]

err, I just tried it again and I must have punched something wrong in my calculator when I squared 100m/s.

Got a value of P₂ = 83.8kPa

 

[SteamKing]

Then Isolated P₂ = P₁ - 1/2pv², using atmospheric pressure for P₁, I solved for the pressure afterwards but it came out to be -560kPa.

Atmospheric pressure is 101.325 kPa. A perfect vacuum is 0 kPa. A pressure of -560 kPa is meaningless.

Now i know taking the absolute value is acceptable with pressures but this number still seems wrong to me.

No, it's not. You also need to establish if your pressure readings are gage or absolute.

 

[Tanner Ross]

Err, we have never discussed gage or absolute pressure in my fluid dynamics class thus far. It is asking what the pressure is as it blows in the wind back into the tunnel from the outside.

 

[SteamKing]

The question was regarding a vacuum suction hose, like a vacuum cleaner. Sorry, didn't specify that part, just typed out the question word for word but didn't realize it didn't mention how the vacuum was being defined as it was defined in the picture.

A perfect vacuum is still 0 kPa absolute or -101.325 kPa gage. These are two bits of data which come in handy when working with fluid flow. :)

 

[Chestermiller]

A perfect vacuum is still 0 kPa absolute or -101.325 kPa gage. These are two bits of data which come in handy when working with fluid flow. :)

The problem statement says that the atmospheric pressure is 90 kPa. That doesn't sound like gauge pressure.

Chet

 

[SteamKing]

Sigh, atmospheric pressure at sea level on Earth is generally recognized to be 101.325 kPa at a temperature of 20°C.

An atmospheric pressure of 90 kPa may be present in the problem's test section, which is also at a temperature of -20°C (Brrr! oo)), but this pressure is rather low to be an ambient condition, unless there is a hurricane or other cyclonic storm present...

 

[Chestermiller]

Sigh, atmospheric pressure at sea level on Earth is generally recognized to be 101.325 kPa at a temperature of 20°C.

An atmospheric pressure of 90 kPa may be present in the problem's test section, which is also at a temperature of -20°C (Brrr! oo)), but this pressure is rather low to be an ambient condition, unless there is a hurricane or other cyclonic storm present...

Yes. That was also my impression. But, that's what they gave.