Lab2_Calculations

Team KAB's Analysis of Lab 2
Data
Calculations for Test 1
Plot Results for the Velocity Profile vs. Radius for the Vertical Plane
Plot Results for the Velocity Profile vs. Radius for the Horizontal Plane
Calculations for Test 2
Test 2 Graph of Mean Velocity of Air vs. Fan Rotational Speed
Test 2 Graph of Total Pressure vs. Fan Rotational Speed
Test 2 Graph of Power Used by Fan vs. Fan Rotational Speed
Calculations for Test 3
Test 3 Graph of Mean Velocity of Air vs. Area Restriction
Test 3 Graph of Total Pressure vs. Area Restriction
Test 3 Graph of Power Consumed vs. Area Restriction

Team KAB's Analysis of Lab 2

Programmer: Aaron Klapheck

% Lab #2 The Axial Fan Test 25-Oct-08
clear, clc, home
fprintf('The date and time: %s \n', datestr(now))

The date and time: 03-Nov-2008 10:17:44

Data

%%%%%% Constants %%%%%%

R = 9; % in, radius of air duct.
rho_man = 999; % kg/m^3, density of water (man short for manometer).
rho_air = 1.225; % kg/m^3, density of air.
g = 9.81; % m/s^2, acceleration due to gravity.
L = 15.76; % in, length of dynamometer lever arm.

% Convert constants to metric %
fprintf('\nInner radius measurement in meters. \n')
R = (0.3048/12).*R % m, radius of air duct.
L = (0.3048/12).*L; % m, length of dynamometer lever arm.



%%%%%% Test 1: Velocity distribution in an air duct. %%%%%%


% The data for test 1 and what it means: %%%%%

% Given the information in the following form:
%   T#_Pt# = [P, UR, LR, RR, LeR]
% How to read this information:
%   T# is the test number (1 in this case).
%   Pt# is the point number (got this information from the data sheet).
%   P is the position of the pilot tube (measured radialy in meters).
%   UR, LR, LeR, and RR are measurements of the velocity pressure heads,
%     hv, (meaused in units of inches of water).
%   UR is the upper radius, LR is the lower radius, LeR is the left radius,
%     and RR is the right radius. Where left and right are in refferece to
%     a vertual eye looking down the tube in the dirrection of air flow.


R1 = .500.*R; R2 = .645.*R; R3 = .764.*R; R4 = .866.*R; R5 = .950.*R;

T1_Pt1 = [R1, 0.21, 0.24, 0.21, 0.21];
T1_Pt2 = [R2, 0.28, 0.27, 0.31, 0.29];
T1_Pt3 = [R3, 0.36, 0.42, 0.40, 0.39];
T1_Pt4 = [R4, 0.42, 0.46, 0.45, 0.46];
T1_Pt5 = [R5, 0.40, 0.40, 0.39, 0.45];

T1 = [T1_Pt1; T1_Pt2; T1_Pt3; T1_Pt4; T1_Pt5];



%%%%%% Test 2: Velocity, total pressure, and power for a 30% opening. %%%%%%


% Given the information in the following form:
%   T#_Pt# = [FS, hv_R1, hv_R2, hv_R3, hv_R4, hv_R5, ht_R1, ht_R2, ...
%               ht_R3, ht_R4, ht_R5, F]
% How to read this information:
%   T# is the test number (2 in this case).
%   Pt# is the point number (got this information from the data sheet).
%   FS is the fan angulare speed (measued in rpm).
%   hc_R1 through hc_R5 are measurements of the velocity pressure heads
%     at each of the five radial distances (measured in units of inches of water).
%   ht_R1 through ht_R5 are measurements of the total pressure heads,
%     at each of the five radial distances (measured in units of inches
%     of water).
%   F is the force the fan exerts on the air passing through it (measured
%   in units of lbf).


T2_Pt1 = [500, .02, .02, .02, .02, .02, .44, .44, .44, .44, .44, 2.6];
T2_Pt2 = [750, .04, .04, .04, .04, .04, .84, .84, .84, .84, .84, 3.0];
T2_Pt3 = [1000, .07, .07, .07, .07, .07, 1.36, 1.36, 1.36, 1.36, 1.36, 3.4];
T2_Pt4 = [1250, .11, .11, .11, .11, .09, 2.5, 2.5, 2.5, 2.5, 2.4, 3.95];
T2_Pt5 = [1500, .16, .16, .16, .16, .14, 3.6, 3.6, 3.6, 3.6, 3.4, 4.8];
T2_Pt6 = [1750, .22, .22, .23, .23, .20, 4.34, 4.34, 4.36, 4.34, 4.3, 6.1];
T2_Pt7 = [2000, .26, .27, .29, .28, .24, 5.52, 5.52, 5.52, 5.48, 5.42, 6.95];

T2 = [T2_Pt1; T2_Pt2; T2_Pt3; T2_Pt4; T2_Pt5; T2_Pt6; T2_Pt7];



%%%%%% Test 3: Velocity, total pressure, and power at 1500 rpm. %%%%%%


% Given the information in the following form:
%   T#_Pt# = [O, hv_R1, hv_R2, hv_R3, hv_R4, hv_R5, ht_R1, ht_R2, ...
%               ht_R3, ht_R4, ht_R5, F]
% How to read this information:
%   T# is the test number (3 in this case).
%   Pt# is the point number (got this information from the data sheet).
%   O is the flow control disk opening size (given as a a decimal between
%     one and zero, where 1 is completly open and 0 is completely closed.
%   hv_R1 through hv_R5 are measurements of the velocity pressure heads
%     at each of the five radial distances (measured in units of inches of water).
%   ht_R1 through ht_R5 are measurements of the total pressure heads,
%     at each of the five radial distances (measured in units of inches
%     of water).
%   F is the force the fan exerts on the air passing through it (measured
%   in units of lbf).


T3_Pt1 = [50, .18, .21, .24, .24, .21, 1.64, 1.68, 1.72, 1.72, 1.68, 4.5];
T3_Pt2 = [40, .18, .19, .21, .20, .18, 1.96, 1.98, 2, 1.98, 1.96, 4.6];
T3_Pt3 = [30, .15, .15, .15, .14, .13, 2.84, 2.84, 2.84, 2.84, 2.82, 4.7];
T3_Pt4 = [20, .04, .06, .08, .10, .09, 2.80, 2.82, 2.84, 2.86, 2.84, 4.3];
T3_Pt5 = [10, .01, .01, .02, .02, .03, 2.80, 2.80, 2.82, 2.82, 2.84, 4.15];
T3_Pt6 = [0, 0, 0, 0, 0, 0, 2.94, 2.96, 2.96, 2.94, 2.94, 4.05];

T3 = [T3_Pt1; T3_Pt2; T3_Pt3; T3_Pt4; T3_Pt5; T3_Pt6];



%%%%%% Convert tests 1 through 3 to metric %%%%%%


% For test 1 convert all inches of water measurements to meters of water.
T1(1:5, 2:5) = T1(1:5, 2:5).*(0.3048/12) % m.

% For test 2 convert all pound measurements to Newtons.
T2(1:7, 12) = T2(1:7, 12).*(4.44822); % N.

% For test 2 convert all inches of water measurements to meters of water.
T2(1:7, 2:11) = T2(1:7, 2:11).*(0.3048/12); % m.

% For test 3 convert all pound measurements to Newtons.
T3(1:6, 12) = T3(1:6, 12).*(4.44822); % N.

% For test 3 convert all inches of water measurements to meters of water.
T3(1:6, 2:11) = T3(1:6, 2:11).*(0.3048/12); % m.

% Get the average values of hv and ht at each fan speed.
T2 = [T2(:,1), mean(T2(:,2:6),2), mean(T2(:,7:11),2), T2(:,12)]

% Get the average values of hv and ht at each area restriction.
T3 = [T3(:,1), mean(T3(:,2:6),2), mean(T3(:,7:11),2), T3(:,12)]

Inner radius measurement in meters. 

R =

    0.2286


T1 =

    0.1143    0.0053    0.0061    0.0053    0.0053
    0.1474    0.0071    0.0069    0.0079    0.0074
    0.1747    0.0091    0.0107    0.0102    0.0099
    0.1980    0.0107    0.0117    0.0114    0.0117
    0.2172    0.0102    0.0102    0.0099    0.0114


T2 =

  1.0e+003 *

    0.5000    0.0000    0.0000    0.0116
    0.7500    0.0000    0.0000    0.0133
    1.0000    0.0000    0.0000    0.0151
    1.2500    0.0000    0.0001    0.0176
    1.5000    0.0000    0.0001    0.0214
    1.7500    0.0000    0.0001    0.0271
    2.0000    0.0000    0.0001    0.0309


T3 =

   50.0000    0.0055    0.0429   20.0170
   40.0000    0.0049    0.0502   20.4618
   30.0000    0.0037    0.0720   20.9066
   20.0000    0.0019    0.0719   19.1273
   10.0000    0.0005    0.0715   18.4601
         0         0    0.0749   18.0153

Calculations for Test 1

fprintf('\n%%%%%% Test 1 %%%%%%\n')

% The calculation of the velocity of the air is done using the equation
% below:
%   v = ((2*rho_man*g*hv)/(rho_air))^(1/2) ... (eqn 1)
% The volumetric flow rate is calculated with the equation below:
%   Q = v_average*pi*R^2 ... (eqn 2)

fprintf('\nUse equation 1 to obtain the velocity. \n')
v_UR = ((2.*rho_man.*g.*T1(1:5, 2))./(rho_air)).^(1/2) % m/s
v_LR = ((2.*rho_man.*g.*T1(1:5, 3))./(rho_air)).^(1/2) % m/s
v_RR = ((2.*rho_man.*g.*T1(1:5, 4))./(rho_air)).^(1/2) % m/s
v_LeR = ((2.*rho_man.*g.*T1(1:5, 5))./(rho_air)).^(1/2) % m/s
radius = T1(1:5, 1) % m.

fprintf('\nCalculate the mean velocity. \n')
v = [v_UR, v_LR, v_RR, v_LeR]
velocity_mean = mean(mean(v)) % m/s

% Calculate the volumetric flow rate.
fprintf('\nUse equation 2 to obtain the volumetric flow rate. \n')
Q = velocity_mean.*pi.*R.^2 % m^3/s

%%% Test 1 %%%

Use equation 1 to obtain the velocity. 

v_UR =

    9.2383
   10.6674
   12.0957
   13.0649
   12.7500


v_LR =

    9.8761
   10.4752
   13.0649
   13.6729
   12.7500


v_RR =

    9.2383
   11.2244
   12.7500
   13.5234
   12.5896


v_LeR =

    9.2383
   10.8563
   12.5896
   13.6729
   13.5234


radius =

    0.1143
    0.1474
    0.1747
    0.1980
    0.2172


Calculate the mean velocity. 

v =

    9.2383    9.8761    9.2383    9.2383
   10.6674   10.4752   11.2244   10.8563
   12.0957   13.0649   12.7500   12.5896
   13.0649   13.6729   13.5234   13.6729
   12.7500   12.7500   12.5896   13.5234


velocity_mean =

   11.8431


Use equation 2 to obtain the volumetric flow rate. 

Q =

    1.9443

Plot Results for the Velocity Profile vs. Radius for the Vertical Plane

% View the Upper and Lower velocity measurements.

R_all = [R1, R2, R3, R4, R5];

for colm = 1:2
    for rows = 1:5
        h = 1;
        if colm == 2
            h=-1;
        end
        if colm == 3 % the third colm are the RR values which need to
                     % appear on the right side (the negative side).
            h=-1;
        end
        x = (0:.1:v(rows,colm)');
        len = length(x);
        if colm <= 2
            z = h.*R_all(rows).*ones(1,len)';
            y = zeros(1,len)';
        else
            y = h.*R_all(rows).*ones(1,len)';
            z = zeros(1,len)';
        end

        plot3(x, y, z, 'LineWidth', 2), ...
        xlabel('Velocity (m/s)'), ylabel('y'), ...
        zlabel('Lower Radius (m)              Upper Radius (m)'), grid on, ...
        view([0,0]), title('Velocity Profile vs. Radius')
        hold on
    end
end

hold off

Plot Results for the Velocity Profile vs. Radius for the Horizontal Plane

% View the Left and Right velocity measurements.

for colm = 3:4
    for rows = 1:5
        h = 1;
        if colm == 2
            h=-1;
        end
        if colm == 3 % the third colm are the RR values which need to
                     % appear on the right side (the negative side).
            h=-1;
        end
        x = (0:.1:v(rows,colm)');
        len = length(x);
        if colm <= 2
            z = h.*R_all(rows).*ones(1,len)';
            y = zeros(1,len)';
        else
            y = h.*R_all(rows).*ones(1,len)';
            z = zeros(1,len)';
        end

        plot3(x, y, z, 'LineWidth', 2), ...
        xlabel('Velocity (m/s)'), ...
        ylabel('Right Radius (m)              Left Radius (m)'), ...
        zlabel('z'), ...
        grid on, ...
        view([0,90]), , title('Velocity Profile vs. Radius')
        hold on
    end
end

hold off

Calculations for Test 2

fprintf('\n%%%%%% Test 2 %%%%%%\n')


% The total pressure is calculated with the equation below:
%   P_tot = rho_man*g*ht ... (eqn 3)
% The power used by the fan can be calculated using the equation below:
%   Power = ((2*pi*N)/60)*F*L ... (eqn 4)

fprintf('\nFan Speeds. \n')
Fan_Speed = T2(:,1)

fprintf('\nUse equation 3 to obtain the total pressure. \n')
P_tot = rho_man.*g.*T2(:,3) % Pa (gage)

fprintf('\nThe velocity head. \n')
hv = T2(:,2) % m

fprintf('\nUse equation 1 to obtain the velocity. \n')
velocity = ((2.*rho_man.*g.*hv)./(rho_air)).^(1/2) % m/s

fprintf('\nUse equation 4 to obtain the fan power. \n')
Power = ((2.*pi.*Fan_Speed)./60).*T2(:,4).*L % W

%%% Test 2 %%%

Fan Speeds. 

Fan_Speed =

         500
         750
        1000
        1250
        1500
        1750
        2000


Use equation 3 to obtain the total pressure. 

P_tot =

  1.0e+003 *

    0.1095
    0.2091
    0.3385
    0.6173
    0.8862
    1.0793
    1.3671


The velocity head. 

hv =

    0.0005
    0.0010
    0.0018
    0.0027
    0.0040
    0.0056
    0.0068


Use equation 1 to obtain the velocity. 

velocity =

    2.8510
    4.0319
    5.3337
    6.5635
    7.9624
    9.4557
   10.4363


Use equation 4 to obtain the fan power. 

Power =

  1.0e+003 *

    0.2424
    0.4196
    0.6340
    0.9207
    1.3426
    1.9905
    2.5919

Test 2 Graph of Mean Velocity of Air vs. Fan Rotational Speed

fprintf('\n%%%%%% Velocity vs. Fan Speed %%%%%%\n')

FitToLine = polyfit(Fan_Speed, velocity, 1);
fprintf('\nVelocity = %g*(FS) + %g \n', FitToLine)
x = [450:0.01:2050];
FitToLine = polyval(FitToLine, x);


plot(Fan_Speed, velocity, 'x', x, FitToLine), ...
    xlabel('Fan Speed (rpm)'), ...
    ylabel('Velocity of Air (m/s)'), ...
    title('Velocity vs. Fan Speed'), ...
    text(900, 4, 'Velocity = 0.0227243*(Fan Speed) + 1.48397 '), ...
    legend('Measurement', 'Line Fit', 'Location','NorthWest')

%%% Velocity vs. Fan Speed %%%

Velocity = 0.00517604*(FS) + 0.192028

Test 2 Graph of Total Pressure vs. Fan Rotational Speed

fprintf('\n%%%%%% Total Pressure vs. Fan Speed %%%%%%\n')

FitToLine = polyfit(Fan_Speed, P_tot, 2);
fprintf('\nTP = %g(FS)^2 + %g(FS) + %g \n', FitToLine)
x = [450:0.01:2050];
FitToLine = polyval(FitToLine, x);

plot(Fan_Speed, P_tot, 'x', x, FitToLine), xlabel('Fan Speed (rpm)'), ...
    ylabel('Total Pressure (Pa)'), title('Pressure vs. Fan Speed'), ...
    text(800, 200, 'TP = 0.000236(FS)^2 + 0.276(FS) + -114'), ...
    legend('Measurement', 'Line Fit', 'Location','NorthWest')

%%% Total Pressure vs. Fan Speed %%%

TP = 0.000236123(FS)^2 + 0.275524(FS) + -114.221

Test 2 Graph of Power Used by Fan vs. Fan Rotational Speed

fprintf('\n%%%%%% Fan Power vs. Fan Speed %%%%%%\n')

FitToLine = polyfit(Fan_Speed, Power, 2);
fprintf('\nPower Consumed = %g(FS)^2 + %g(FS) + %g \n', FitToLine)
x = [450:0.01:2050];
FitToLine = polyval(FitToLine, x);

plot(Fan_Speed, Power, 'x', x, FitToLine), xlabel('Fan Speed (rpm)'), ...
    ylabel('Fan Power Consumed (W)'), title('Power vs. Fan Speed'), ...
    text(850, 380, 'Power Consumed = 0.000868(FS)^2 + -0.614(FS) + 356 '), ...
    legend('Measurement', 'Line Fit', 'Location','NorthWest')

%%% Fan Power vs. Fan Speed %%%

Power Consumed = 0.000868409(FS)^2 + -0.614013(FS) + 356.62

Calculations for Test 3

fprintf('\n%%%%%% Test 3 %%%%%%\n')


% The power used by the fan can be calculated using the equation below:
%   Power = ((2*pi*N)/60)*F*L ... (eqn 5)

Fan_Speed = 1500; %rpm, constant for this test

fprintf('\nPercent area restriction. \n')
area = 100-T3(:,1)

fprintf('\nUse equation 3 to obtain the total pressure. \n')
P_tot = rho_man.*g.*T3(:,3) % Pa (gage)

fprintf('\nThe velocity head. \n')
hv = T3(:,2) % m

fprintf('\nUse equation 1 to obtain the velocity. \n')
velocity = ((2.*rho_man.*g.*hv)./(rho_air)).^(1/2) % m/s

fprintf('\nUse equation 5 to obtain the fan power. \n')
Power = ((2.*pi.*Fan_Speed)./60).*T3(:,4).*L % W

%%% Test 3 %%%

Percent area restriction. 

area =

    50
    60
    70
    80
    90
   100


Use equation 3 to obtain the total pressure. 

P_tot =

  420.1851
  491.8755
  705.9508
  704.9551
  700.9723
  733.8304


The velocity head. 

hv =

    0.0055
    0.0049
    0.0037
    0.0019
    0.0005
         0


Use equation 1 to obtain the velocity. 

velocity =

    9.3693
    8.8335
    7.6500
    5.4840
    2.7047
         0


Use equation 5 to obtain the fan power. 

Power =

  1.0e+003 *

    1.2587
    1.2866
    1.3146
    1.2027
    1.1608
    1.1328

Test 3 Graph of Mean Velocity of Air vs. Area Restriction

fprintf('\n%%%%%% Velocity vs. Area Restriction %%%%%%\n')

FitToLine = polyfit(area, velocity, 2);
fprintf('\nVelocity = %g(AR)^2 + %g(AR) + %g \n', FitToLine)
x = [48:0.01:102];
FitToLine = polyval(FitToLine, x);


plot(area, velocity, 'x', x, FitToLine), ...
    xlabel('Area Restriction (%)'), ...
    ylabel('Velocity of Air (m/s)'), ...
    title('Velocity vs. Area Restricted'), ...
    text(48, 2, 'Velocity = -0.00307(AR)^2 + 0.2689(AR) + 3.71 '), ...
    legend('Measurement', 'Line Fit')

%%% Velocity vs. Area Restriction %%%

Velocity = -0.00307636(AR)^2 + 0.268885(AR) + 3.70897

Test 3 Graph of Total Pressure vs. Area Restriction

fprintf('\n%%%%%% Total Pressure vs. Area Restriction %%%%%%\n')

FitToLine_a = polyfit(area(1:2), P_tot(1:2), 1);
fprintf('\nTotal Pressure = %g*(Area Restricted) + %g \n', FitToLine_a)
x_a = [40:0.01:61];
FitToLine_a = polyval(FitToLine_a, x_a);

FitToLine_b = polyfit(area(3:6), P_tot(3:6), 2);
fprintf('\nTotal Pressure = %g*(Area Restricted) + %g \n', FitToLine_b)
x_b = [69:0.01:110];
FitToLine_b = polyval(FitToLine_b, x_b);

plot(area, P_tot, 'x', x_a, FitToLine_a, x_b, FitToLine_b), ...
    xlabel('Area Restriction (%)'), ...
    ylabel('Total Pressure (Pa)'), ...
    title('Pressure vs. Area'), ...
    legend('Measurement', 'Line Fit 1', 'Line Fit 2','Location','NorthWest')

%%% Total Pressure vs. Area Restriction %%%

Total Pressure = 7.16903*(Area Restricted) + 61.7334 

Total Pressure = 0.0846344*(Area Restricted) + -13.5913 

Total Pressure = 1244.62*(Area Restricted) +

Test 3 Graph of Power Consumed vs. Area Restriction

fprintf('\n%%%%%% Fan Power vs. Area Restriction %%%%%%\n')

FitToLine_a = polyfit(area(1:3), Power(1:3), 1);
fprintf('\nTotal Pressure = %g*(Area Restricted) + %g \n', FitToLine_a)
x_a = [40:0.01:71];
FitToLine_a = polyval(FitToLine_a, x_a);

FitToLine_b = polyfit(area(4:6), Power(4:6), 1);
fprintf('\nTotal Pressure = %g*(Area Restricted) + %g \n', FitToLine_b)
x_b = [79:0.01:110];
FitToLine_b = polyval(FitToLine_b, x_b);

plot(area, Power, 'x', x_a, FitToLine_a, x_b, FitToLine_b), ...
    xlabel('Area Restriction (%)'), ...
    ylabel('Fan Power Consumed (W)'), ...
    title('Power vs. Area'), ...
    legend('Measurement', 'Line Fit 1', 'Line Fit 2')

%%% Fan Power vs. Area Restriction %%%

Total Pressure = 2.79702*(Area Restricted) + 1118.81 

Total Pressure = -3.49628*(Area Restricted) + 1480.09

Contents

Team KAB's Analysis of Lab 2

Data

Calculations for Test 1

Plot Results for the Velocity Profile vs. Radius for the Vertical Plane

Plot Results for the Velocity Profile vs. Radius for the Horizontal Plane

Calculations for Test 2

Test 2 Graph of Mean Velocity of Air vs. Fan Rotational Speed

Test 2 Graph of Total Pressure vs. Fan Rotational Speed

Test 2 Graph of Power Used by Fan vs. Fan Rotational Speed

Calculations for Test 3

Test 3 Graph of Mean Velocity of Air vs. Area Restriction

Test 3 Graph of Total Pressure vs. Area Restriction

Test 3 Graph of Power Consumed vs. Area Restriction