

Subject:
Calculating thrust for a fan
Category: Science > Physics Asked by: ahmed333ga List Price: $10.00 
Posted:
29 Jun 2004 12:19 PDT
Expires: 29 Jul 2004 12:19 PDT Question ID: 367795 
A fan (five blades, each blade = 225 mm) diameter = 600 mm Speed = 2850 RPM Air flow = 4.5 m^3/s Air temperature = 50 C Pressure in inlet of the fan = 1 atmospheric Pressure Operate at 100 m above sea level I want to know the thrust (force) that this fan is making and how to calculate it.  


There is no answer at this time. 

Subject:
Re: Calculating thrust for a fan
From: saem_aeroga on 30 Jun 2004 11:03 PDT 
There are many computational, experimental, and analytical ways of obtaining thrust from fans. Take a deep breath  I'm going to quickly give you ideas of all three. It is important to know if the fan is in a duct or in a freeair environment. 1. Blade element theory as given in the clarification was designed for making new airfoil shapes. Yes they have designed fan shapes using this method. However it is not accurate for determining engineering data  I have tried designing airfoils with BET and it can give approximate designs. Today noone uses BET for design unless its in the classroom. The easiest way to figure out the thrust is with the Reynold's transport thereom (analytical method). You can go to any library, pick up a book on Fluid Mechanics and use this theory. You have all the data you need to make a calulation. It would be best if you knew the AVERAGE inflow velocity and AVERAGE outflow velocity, The diameter of the fan, and the density. (you just don't have the inflow velocity unless you assume it is zero upstream) 2. You can use a computational method. This would be a very expensive simulation. Depending on the details of the simulation you can decide to use anythhing from a simple Euler calculation to a full navier stokes simulation with turbulence modeling. However your simulation could only use what we call a zero equation turbulence model... currently when we figure out the flow fields past aircraft we use this class of turbulence models because of the lack of computer power. Its all very complicated... :( I recommend checking out www.cdadapco.com or www.fluent.com for information on commercial software packages that can perform these things. Although they are general codes they may perform a wide range of simulations (jack of all trades syndrome). 3. Experimental  You can mount the fan in a laboratory and put a force transducer on the mount. Turn on the fan and it will measure the force. That is the easiest way to measure the thrust! The same technique is done to measure the force of the new hybrid rocket engines. :) however if you don't have a force transducer (they aren't expensive) then you can put the fan in front of a hanging board. Hang the board from the cieling. Make sure that it swings freely. Put the fan in front of the board and turn it on. You can then measure the average angle that the board has turned away from the verticle (fan off) position. Using this angle and the Reynol'ds transport thereom you can find the force to a pretty accurate level. good luck. 
Subject:
Re: Calculating thrust for a fan
From: wil_e_davinciga on 03 Jul 2004 03:31 PDT 
there ARE a lot more "dimensions" necessary for a more exact answer, but if you want a ballpark figure, ThrustHP is a small piece of freeware for modelers that will actually allow any diameter prop to be input... not POSITIVE of the math behind it, some people say it's accurate and a few don't... some basic inputs, ie 24in diameter, pitch of 15(guess) 2 blades(and extrapolate to 5) rpm of 2850, and i use master airscrew for the prop, yields an efflux velocity of 40.48 mph, .823hp (*2.5 for 5 blades for 2.06 hp) and 7.63 lbs thrust (*1.9 for 5 blades for 14.5 lbs)... and know that an increase in pitch increases efflux and hp linearly, and an increase in rpm increases; efflux by (rpm2/rpm1), thrust by (rpm2/rpm1)^2, and hp by (rpm2/rpm1)* 2^(rpm2/rpm1), and an increase in diameter increases thrust and hp by (dia2/dia1)^4... the diameter one i think is where the math might not take into account an increase in chord as well as an increase in span, so it isn't really working for ducted fans if that's your app (ie, hovercraft/ helio) well, good luck, and if you find some software that does it better, lemme know :D ps, there's also a sight for a guy who converted a varieze plane to rotary engine and rear ducted fan, and he has lots of sets of data on his sight, but it's more like a 37.5" fan, http://www.bridgingworlds.com/DUCKT.HTM 
Subject:
Re: Calculating thrust for a fan
From: nikyzfga on 09 Jul 2004 09:19 PDT 
We have the temperature, atmospheric pressure, and air flow, so do we need to know anything about the blades? I don't know the formula, but wouldn't the mass of air being blown gives us all we need to derive thrust? 
Subject:
Re: Calculating thrust for a fan
From: upstartaudioga on 15 Jul 2004 07:02 PDT 
I agree with nikyzfga. There appears to be enough information here to solve the problem. First, use the information given in the problem to establish that the blades of the fan are subsonic. From the information given, the tips of the blades are moving at about 90 m/sec, so we establish that the blades are moving much slower than the speed of sound (330 m/sec). Whatever dynamics are at work, we don't need to consider supersonic effects, pressure waves, etc. Ignoring the question of blade profiles (for which we don't have enough information) for the moment, consider the inlet pressure. If the inlet pressure of 1 atm is accurately measured, we might try to solve the problem this way: From a table at http://www.usatoday.com/weather/wstdatmo.htm we can get the standard atmospheric conditions for 15C and sea level: Height Temperature Pressure Density (m) (C) (hPa) (kg/m3) 0000 15.0 1013 1.2 1013 hPa is exactly one standard atmosphere. Now I take a leap of faith and assume that atmospheric pressure should obey the ideal gas law, and make a correction for the pressure we lose by climbing 100m. If those assumptions are valid, at 100m altitude and a temperature of 50C, the pressure should be something like: (1*atm  (100m * 1.2 kg/m^3) * g) * 323/298 = 1.11 atm where 1*atm is standard pressure 100m is our altitude 1.2 kg/m^3 is the approximate density of air at sea level 323/298 is the difference in absolute temperature from 15C to 50C g is the gravitational constant for earth 9.8 m/sec^2 Then, since the problem states that the inlet pressure is only 1.0 atm, we can assume that the fan has created a pressure differential of 0.11 atm. Multiplying this pressure by the area of the fan, we get: 0.11*atm * 0.283 m^2 = 700 lbf. I haven't been very rigorous here, but then that's what you get for a free answer. Perhaps a researcher interested in grabbing the prize could verify or discredit the above? I must admit, I don't know whether we should double the force above to account for both the vacuum in front and increased pressure behind the fan, or if we should only count it once. Dividing the flow rate of 4.5 m^3/sec by the area of .283 m^2, we have a linear velocity of about 16 m/s or 36mph. Assuming we only count the pressure once, for the given force of 700 pounds, you would need to drive 70hp into the fan. Otherwise, double the horsepower too. Is there a physics professor out there with the answer? 
Subject:
Re: Calculating thrust for a fan
From: racecarga on 21 Jul 2004 17:48 PDT 
78 Newtons or 17.5 lb. All you need to know is A) the rate at which air is being moved, in terms of mass per unit time and B) the velocity with which the air leaves the fan. Multiply these together, and you have your thrust. A) is given by 4.5 m^3 / s times the density of air at 50C and 100 m above sea level, which is about 1.09 kg/m^3. So air is blown at a rate of about 4.9 kg/s. To get the velocity, you divide the volume rate of flow by the area of the fan, which is pi*(.3)^2 (the radius of the fan is 0.3 m). So the velocity is about 15.9 m/s. 4.9 kg/s * 15.9 m/s gives 78 kg m/s^2, or 78 N. The way to understand this is to realize that force is just the rate of change of momentum with time. So if you take the momentum given to air in a time interval, and divide the the length of that time interval, you get the force. The momentem given to the air is just the mass of the air times the velocity of the air. 
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