Great video! The way I interpret the equation from the EPA is that you want to calculate the square roots of your delta P for each point, sum them up, and square the result. Then you plug that number into your equation which you will have to divide by your number of points (n). You will get a very small difference in results compared with calculating velocity per point and average them all out. I think it has to do with the quadratic dependence of velocity on differential pressures but am not 100% sure. It also helps with capturing variations in your "data set" if you have low or high pascal readings at some of the points. Would be great to get your opinion on that.
Hi Jordan, I agree with your interpretation of USEPA M2 Section 12.6 except for where you mention square the sum of the roots again? Velocity is not related to the pressure drop exponentially but to its inverse. if I check the math it should reduces to the same as the average of all the velocities, but perhaps you can spot a mistake in my arithmetic: Let us assume we have 3 points to simplify (You can do the math with 6 too): 12.6 reads: Vs=KpCp*SQRT(Ts/ (PsMs) ) *SUM( SQRT(detla P) ) / n Now let A= KpCp*SQRT(Ts/(PsMs)) to simplify writing For our 3 points: Vs=A * SUM(SQRT(delta Pi)*(1/n) Vs= A*( SQRT(detla P1) + SQRT(detla P2)+SQRT(detla P3) )/3 We can separate the terms: Vs=A*SQRT(detla P1)/3 + A*SQRT(detla P2)/3+ A*SQRT(detla P3)/3 Here each term is a velocity at the point, so: Vs= V1/3+V2/3+V3/3 = (V1+V2+V3)/3 = Average of the 3 point velocities?
On a side note, this is not the best way to determine a stack gas velocity, or rather USEPA Method 1 is not. Applying the1/7th power law offers a much better representation of the average velocity.
With Type 1 pitot: The reading is the dynamic pressure + static pressure. Thus the differential pressure reading - the static pressure will give you the dynamic pressure. The static pressure can be measured by the Type 1, through removing the + leg. With type S: Dynamic pressure = 0.84(or your factor)^2 x Differential pressure reading.
The exact method may vary based on legislative requirements in your region, but we measure in accordance with the USEPA's procedures. Method 1 describes where the measurements should be made and how to calculate the traverse points, see www.epa.gov/emc/method-1-samplevelocity-traverses
Great video! The way I interpret the equation from the EPA is that you want to calculate the square roots of your delta P for each point, sum them up, and square the result. Then you plug that number into your equation which you will have to divide by your number of points (n). You will get a very small difference in results compared with calculating velocity per point and average them all out. I think it has to do with the quadratic dependence of velocity on differential pressures but am not 100% sure. It also helps with capturing variations in your "data set" if you have low or high pascal readings at some of the points. Would be great to get your opinion on that.
Hi Jordan, I agree with your interpretation of USEPA M2 Section 12.6 except for where you mention square the sum of the roots again? Velocity is not related to the pressure drop exponentially but to its inverse.
if I check the math it should reduces to the same as the average of all the velocities, but perhaps you can spot a mistake in my arithmetic:
Let us assume we have 3 points to simplify (You can do the math with 6 too):
12.6 reads:
Vs=KpCp*SQRT(Ts/ (PsMs) ) *SUM( SQRT(detla P) ) / n
Now let A= KpCp*SQRT(Ts/(PsMs)) to simplify writing
For our 3 points:
Vs=A * SUM(SQRT(delta Pi)*(1/n)
Vs= A*( SQRT(detla P1) + SQRT(detla P2)+SQRT(detla P3) )/3
We can separate the terms:
Vs=A*SQRT(detla P1)/3 + A*SQRT(detla P2)/3+ A*SQRT(detla P3)/3
Here each term is a velocity at the point, so:
Vs= V1/3+V2/3+V3/3 = (V1+V2+V3)/3 = Average of the 3 point velocities?
On a side note, this is not the best way to determine a stack gas velocity, or rather USEPA Method 1 is not. Applying the1/7th power law offers a much better representation of the average velocity.
How we ensure the pitot tube exactly in the correct plan of flow
How to calculate dynamic pressure?
With Type 1 pitot:
The reading is the dynamic pressure + static pressure. Thus the differential pressure reading - the static pressure will give you the dynamic pressure. The static pressure can be measured by the Type 1, through removing the + leg.
With type S: Dynamic pressure = 0.84(or your factor)^2 x Differential pressure reading.
cp^2 x deltaP
How do you know where to take the measurements?
The exact method may vary based on legislative requirements in your region, but we measure in accordance with the USEPA's procedures. Method 1 describes where the measurements should be made and how to calculate the traverse points, see www.epa.gov/emc/method-1-samplevelocity-traverses
Why are pitot tubes used and not anemometers?
Thermocouples are simple with no moving parts. Vane anemometers can't handle the temperatures and the corrosive nature of most flue gasses