Plot the stream function for the flow Y = x^2 - z^2. Assume that the values of the stream function are already obtained before hand and only plotting is to be done. Also plot velocity potential function over the stream function plot.
clear all; [x z] = meshgrid(0:0.04:3); velocitypotential = x.^2 - z.^2; contourf(x,z,velocitypotential,100); title('Contours of Velocity Potential'); set(gca,'fontsize',20); hold on; figure(2); [x z] = meshgrid(0:0.08:3); velocitypotential = x.^2 - z.^2; contourf(x,z,velocitypotential,100); title('Contours of Velocity Potential'); set(gca,'fontsize',20); hold on; startx = 0:0.08:3; starty = 0:0.08:3; u = -2*x; w = 2*z; streamline(x,z,u,w,startx,starty); title('Contour Plot of Velocity Potential with Streamlines'); figure(3); streamline(x,z,u,w,startx,starty); hold on; quiver(x,z,u,w,1.5); set(gca,'fontsize',20); title('Streamlines with Velocity Vectors');
Find the components of the vector of magnitude 20 making an angle 30 degree with the x-axis.
Here, we need to determine the horizontal and vertical components of the vector. Imagine the vector to be the hypotenuse of a triangle in which the height of the triangle corresponds to the y-axis component and base corresponding to the x-axis component. Then, the components of the vector are given by x component = 20 x cos(30) y component = 20 x sin(30) Substitute for cos(3) and sin(30) to get the required answer. That I am leaving up to you!
Discuss the effect of camber on the lift-curve slope, the zero-lift angle of attack and the drag curve.
Camber does not alter the lift curve slope, according to thin airfoil theory. However, it affects the zero lift angle of attack. Positive camber makes the zero lift angle of attack negative (i.e., it shifts the lift curve to left) and a negative camber makes zero lift angle of attack positive negative (i.e., it shifts the lift curve to right) .The effect of camber on drag is rather complicated. An efficient camber reduces the drag on the airfoil. However if the camber is not designed properly, it can lead to a lot more drag than a similar airfoil without camber.