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de oppresso liber
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Discussion Starter · #1 ·
I have looked some but can't find an answer so I thought some windmill types might know.

How do you calculate the energy and pressure on an object by using the wind speed? There has to be some equations for this but I can't find them. I'm not talking about some differential equation from fluid dynamics where you need to know the density of the air and the ballistic coefficient of the object. I'm talking nice simple 'air' blowing against something flat equations.

Say you have a 4 by 4 sheet of plywood placed perpendicular to the air flow. How much energy would be acting on it if the wind speed was 5 mph? Assuming the pressure were equal over the entire area, which it wouldn't be, what would be pressure per unit of area be?
 

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What you want is force caused by drag.

To calculate you will need density of air (1.2kg/cu m) and the drag coefficient (Cd) of a flat plate (1.28).

Use F=1/2*density*Vel squared*area*Cd

I came out with about 5 lbs

Look at coefficient of drag in Google or Wiki
 

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Here is a table giving the force on a flat surface in pounds per square foot or per square inch, for wind speeds in miles per hour. According to it, a 5mph wind is equivalent to 0.064 psf wind load. This is used in building code requirements.
 

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I think Jim is right....must have lost something between MKS and English translation.

Here's an easy formula for force in pounds using ft and MPH.

F=Velocity(in mph) squared times area(in sq ft) divided by 390

For 16 sq ft at 5mph I get 1.026 lbs.

Jim's .064 psf over 16 sq ft is 1.024 lbs.
 

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de oppresso liber
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Discussion Starter · #5 ·
Ok let's see if I've got it.

F is the force
Da is the air density given as 1.2 kg/m^3
Va is the speed of the air in m/sec
Cd is the coefficient of drag given as 1.28 for a flat surface
A is the area of the flat surface in m^2

F = 1/2 * Da * Va^2 * A * Cd

or

F = 1/2 * 1.2 * Va^2 * A * 1.28 = 0.768 * Va^2 * A

If my math works we wind up with kg-m/sec^2 which just happens to be Newtons which is a unit of force.

So let's crank some numbers. (all conversions from onlineconversion.com to reduce my math errors)

A = 16 ft^2 = 1.5 m^2
V = 5 mph = 2.2 m/sec
F = 0.768 * V^2 * A

0.768 * 2.2^2 * 1.5 = 5.6 N or 1.3 pound-force

Seems like a lot more when you are trying to move a half sheet of plywood in a breeze.
 

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Ok what about if we change the question to water at 3mpg? I interested in a area of 8 feet diameter halfed so it would be 4 squared x pi about 25 square feet right?
Then the desity of water would be 64 Lbs/ft x velocity squared (3x3=)9 X area of 25 times Cd of 1.28
so
64x9x25x1.28
or about 18432 ft/pounds of force?
Wow that sounds like a LOT!
 

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A few things:

Density is mass/volume, and the English unit of mass is a slug, pounds are a force. F=ma so to find the mass we divide by the acceleration. In weight measurement (lbs), acceleration due to gravity (32ft/sec sq) is included, so to find the mass in slugs divide weight in pounds by 32. Water density is about 2 slug/cu ft.

Units must be consistent, so convert 8 mph to 11.7 ft/sec
(multiply by 5280 /3600)

Area in sq ft=pi R squared=50.24 sq ft

Or 8760 lbs

Hope I did all my math right...seemed to check OK
 

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Ill only be able to use Half of the area so about 25 square feet , but even reducing your number by half works out to 4380 lbs and that STILL seems like a lot!

Good greif Im gonna have to build this thing STOUT!
 
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