Friday, November 22, 2013

Inches of Stuff

In the US we are still stuck on inches, feet and miles.  The French who traded with lots of different nations that used lots of different units decided they wanted a simpler "universal" system and developed the metric system based on the length of the meridian through Paris in a blatant case of prime meridian envy.  While the miscalculated that a touch, their metric units made it to the big time.

Still we in the US like things like inches.  If there was an inch of rain, there was about 2.42 centimeters of rain.  If that inch of water applied a pressure, then it applied about 0.0024558598569 atmospheres of pressure.  One atmosphere of pressure is then about 407 inches of water or about 33.92 feet of water. If you build a water barometer it would have to be at least 34 feet tall which is a little inconvenient so most liquid barometers are filled with Mercury so they would only have to be about 30 inches tall.

I bring this up because I have used both Mercury and water (spirits most of the time so no algae grows) to test pressure in air systems.  One inch of water as a differential pressure measured using a Pitot tube is about 4005 feet per minute and the air velocity increases as the square root of the differential pressure.

There are the typical caveats about STP, standard temperature and pressure which is typically one atmosphere and ~70 degree F, another archaic units we in the US cling to more out of tradition than necessity.

Around the Globe, the average wind velocity is about 12 miles per hour which is (12*5280feet/mile)/60minutes/hour or about 1006 FPM.  You can just imagine that 4005FPM is about .758 miles per minute or about 45 mph.  The average differential pressure for 12 mph would be lower by the square root of the pressure ratio or the differential pressure the square of the velocity ratio.  (1006/4005)^2=0.063 in. W.C. which is inches of water column. This is part of the Fan Laws which is more correctly called the Affinity Laws.

What is cool is that the fan laws are so simple that whatever units you prefer, you only have to remember one reference velocity and pressure then you can calculate your butt of with the best of them.   There are things you have to be aware of, if you really want to be a fluid flow hot shot, but the Fans Laws are the backbone of fluid dynamics.

To measure air flow differential pressure you need some standard like a Pitot tube and a U-tube or inclined manometer.

The Engineering Toolbox has one of their typically stellar write ups on the Pitot tube plus this diagram.

You have the static pressure hs, total pressure ht and what you want for velocity is hd or the differential pressure.  Once you have all that tested, as long as the system is constant, meaning you don't restrict or improve flow downstream of the "traverse" point you have an air flow monitoring station or reference if you have a reliable static pressure probe installed.

If you want to get fancy you can install an orifice plate or a venturi flow meter which can amplify the differential pressure for more accuracy or just a stack of bricks if you are a cheap skate with a differential pressure across the bricks.  Nothing to it.  Then the reference is completely independent of the total static pressure.  Note that total static pressure is not the same as just old static pressure since it includes the velocity pressure.  You can use total static or static as long as both sides of you bricks measure the same thing.  The "same" thing tends to throw some people off.

Orifice Plates and Venturi Flow meters use known changes is velocity pressure to measure the air flow.  If you know the area change and the performance characteristic of the meter and fluid, you have a high quality and very accurate measuring station based on the difference in total static pressure and static pressure.  Since they are based on the difference, the measurements are independent of the total pressure up to the limit where the operating temperature and pressure impact the characteristics, Density, Viscosity and Phase of the fluid plus there can be some laminar versus turbulent flow issues if you over size or under sized the orifice.

Neglecting the velocity component of the total static pressure was a common problem with variable air volume components back in the day.  If you have 1 inch of static pressure available and required a velocity pressure of 1 inch (45mph velocity), you never got what you wanted.  You needed the 1 inch plus the losses downstream of the restriction.  So a lot of systems never would work quite right without some TLC, like enlarging the entrance duct to allow static regain which is nothing more than reducing velocity so that the velocity pressure reverts to static pressure, smoothing approaches or increasing the fan RPM, BHP and system TSP which increased operating cost and noise levels which was not a good thing.  Some people would over compensate which resulted in an extremely quiet but expensive system.  It is always better to get it closer to right the first time.  So know your fan laws if you want to play with fluid flows.

The reason I have this post is because one of the local denizens is making the simple mistake of assuming that as long as the static pressure is fixed, the average velocity pressure is fixed.  Nope.  Velocity pressure is dependent on the differential pressure which has a lot more involved than just atmospheric pressure and temperature.

For example the Southern Oscillation Index (SOI) is based on the monthly average sea level pressure between Tahiti and Darwin using the formula 10x((average monthly Tahiti MSLP)-(average monthly Darwin MSLP))/(long term standard deviation of difference for month) which amplifies the monthly deviation by a factor of ten.  Since the MSLP is typically in millibars and there are a few minor variations on depending on baseline selection and the need to use the 10 multiplier, but the base differential pressures are the same.

Tahiti is located at Latitude:17 32 S Longitude:W 149 34 W  and Darwin at 12 28 S 130 50 E

Using the KNMI Climate Explorer and the Kaplan Surface pressure reconstruction I put together this chart for the Tahiti and Darwin areas, this is not the exact match to the SOI since the areas are 20 degree longitude bands by 10 degree latitude bands roughly centered on each reference area.  Each of the series has a long term trend related to general shifting of climate related to the Inter-Tropical Convergence Zone (ITCZ) or shift in the Earth's Thermal Equator.  J. R. Toggweiler with the Geophysical Fluid Dynamic Laboratory (GFDL) has an excellent easy to read paper on the subject called Shifting Westerlies

Toggweiler is mainly an ocean modeler and tries to related a good deal of his work to paleoclimatology which for some reason tends to through people off.  Paleo is our reference to the past and if it happened before, especially recently, it is likely to happen again.  So hundred year and longer climate shifts being confused with some other "forcing" like CO2 for example, will likely happen again.

Now as far as "weather" goes, using the fans laws to predict wind velocity gets you in the ballpark but all those other things that have to remain equal are lurking.  For example a super typhoon/hurricane might have a central pressure of 890 mb which compared to "normal" of about 1010 mb would be a 120mb low or ~48 in. W.C. of differential pressure.  Using the basic fan law formula the maximum velocity would be about 311 mph or about 275 knots.  How tight the pressure gradient is makes a large difference, but I you have four foot of water pressure differential you have yourself some serious winds.

Differences in saturation vapor pressure is still a pressure differential which is enough to enhance summer sea breezes and the afternoon thunderstorms common on the coasts.  It only takes an inch of pressure differential and the wind itself creates as lower local pressure which increases surface evaporation helping the storms intensify.  Luckily these dynamic processes tend to destroy themselves or life might be way too interesting.  It don't take much to get the ball rolling though.