# Differences Between Pressure Distribution On Smooth Surface Between A Cylinder

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Aim In this experiment, we aim to compare the differences in pressure distribution on a smooth surface between a cylinder that its axis is placed perpendicular to the flow and a cylinder with frictionless flow. And hence, we would be able to calculate the drag coefficient for that cylinder using the data we collect from the experiment. Introduction Firstly using the Bernoulli’s equation, we can explain the relationship between the pressure of a fluid and its velocity for two points that lie on the same single streamline.  P_1/(ρ_air g)+(V_1^2)/2g+Z_1=P_∞/(ρ_air g)+(V_∞^2)/2g+Z_2 [Eq. 1] As height will remain constant in a wind tunnel experiment, so gravitational force is eliminated. P_1+(ρ_air V_1^2)/2=P_∞+(ρ_air V_∞^2)/2 The velocity of fluid becomes zero at stagnation point when the pressure tapping 1 is at ∅=0, as the surface of the cylinder is now perpendicular to the flow, hence the dynamic pressure is: (ρ_air V_∞^2)/2=P_1-P_∞ Hence, P_1=P_atm+ρ_ms g(h_a-h_1 )sinβ P_∞=P_atm-ρ_ms g(h_∞-h_a )sinβ And by substituting the above 3 equations, P_1-P_∞=ρ_ms g(h_∞-h_1 )sinβ=(ρ_air V_∞^2)/2 [Eq. 2] And we can find the upstream dynamic pressure of the cylinder using, (ρ_air V_∞^2)/2=K〖∆P〗_betz=Kgρ_water 〖∆h〗_betz [Eq. 3] Where K is the tunnel calibration constant and 〖∆P〗_betz is the difference in pressure across the contraction of the wind tunnel that can be read from the