# Pressure coefficient over a flat plate against its length/width ratio

We conducted an experiment to measure the surface pressure distribution around a flat plate (dimensions below). The plate has 104 equally distributed tappings as shown below. Where the arrows indicate order of measurement.

I would like to plot the pressure coefficient against length(L) to width(W) ratio L/W

The following data is the pressure recorded clockwise (as suggested by the diagram) at the corresponding tap. Saved in a file called "combined_pressures.txt".

The first four rows are pressure data over the upper part of the plate, while the other four rows contain pressure data over the lower part of the plate.

First row from tap 0 to upper tap 12, second row from upper tap 13 to upper tap 25, third row from upper tap 26 to upper tap 38, fourth row from upper tap 39 to upper tap 51, fifth row from tap 52 to lower tap 40, sixth row from lower tap 39 to lower tap 27, seventh row from lower tap 26 to lower tap 14, eighth row from lower tap 13 to lower tap 1.

100.016 -15.341 -24.538 -29.053 -31.768 -32.851 -33.200 -33.873 -33.885 -33.219 -32.734 -33.104 -32.086

98.884 -16.562 -25.100 -29.238 -31.768 -32.662 -32.833 -33.473 -33.504 -32.833 -32.317 -32.712 -31.540

-30.698 -29.985 -27.909 -26.277 -24.625 -22.845 -20.910 -20.444 -19.227 -17.962 -17.722 -18.021 -17.137

-16.762 -17.085 -16.109 -16.469 -17.106 -17.181 -16.875 -17.638 -17.704 -17.575 -17.722 -19.000 -18.960

-19.587 -20.746 -20.792 -22.206 -24.061 -26.243 -28.981 -35.477 -32.742 -31.288 -31.274 -32.124 -31.540

-31.829 -32.426 -31.656 -31.828 315.657 -32.851 -36.318 -30.867 -27.032 -24.142 -22.726 -22.330 -20.601

-19.587 -19.525 -17.982 -17.950 -17.670 -17.370 -16.508 -16.836 -16.562 -16.223 -16.263 -17.237 -16.772

-16.950 -17.433 -16.671 -17.025 -17.482 -18.125 -18.159 -19.643 -20.559 -22.017 -24.185 -28.402 -30.628

I used the following MATLAB code

% Define plate dimensions

plate_length = 0.225; % m

plate_width = 0.025; % m

% Load pressure data from the text file

% Split the data into upper and lower parts

num_points = size(pressure_data, 2); % Number of pressure data points

% Define freestream conditions

P_infinity = 101984*(1/101325); % bars

rho = 1.225; % kg/m^3 (air density)

V = 14; % m/s (freestream velocity)

% Define the chord length

chord_length = plate_length + plate_width;

% Calculate the length-width ratio for each data point

length_width_ratio = chord_length * (1:num_points) / num_points;

% Calculate pressure coefficients for upper and lower parts

Cp_upper = (pressure_data(1, :) - P_infinity) / (0.5 * rho * V^2);

Cp_lower = (pressure_data(5, :) - P_infinity) / (0.5 * rho * V^2);

% Create a plot

figure;

plot(length_width_ratio, Cp_upper, 'r', 'DisplayName', 'Cp top');

hold on;

plot(length_width_ratio, Cp_lower, 'b', 'DisplayName', 'Cp bottom');

xlabel('Length-Width Ratio');

ylabel('Pressure Coefficient (Cp)');

legend('Location', 'Best');

title('Pressure Coefficient vs. Length-Width Ratio');

grid on;

END of MATLAB code

Which yields This is not what I expected. I expected a plot similar to the following I am wondering whether I made a mistake with the code or it's due to faulty experimental data.

Thanks.

• Three questions: 1) why do you calculate the chord as being "chord_length = plate_length + plate_width"? Shouldn't chord simply be plate_lenght? 2) Why do you use the pressures only from the first and the fifth row of your txt file: "Cp_upper = (pressure_data(1, :) - blabla; Cp_lower = (pressure_data(5, :) - blabla"? TBC Oct 10 at 20:26
• 3) Have you taken into account that the taps are arranged/stored from leading to trailing edge on the upper surface and the other way around on the lower surface? Plus, as already pointed out by @RobMcDonald, being the plate symmetrical and at 0° angle of attack, the pressure distribution on the top and on the bottom should be symmetrical and close to 0 Oct 10 at 20:26