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Drag on a Cylinder

Consider a real fluid flowing past a cylinder of a diameter D and length L with uniform velocity U.

(i)    When Re < 1, the drag force is directly proportional to velocity and hence coefficient of drag is inversely proportional to Reynolds number.

(ii)    When Re between 1 to 2000, the drag force decrease and reaches a minimum value of 0.95 at Re = 2000.

(iii)    When Rc is increase from 2000 to 3 x 104 , the coefficient of drag increases and attains maximum value CD = 1.2 at Re = 3x104.

(iv)    When Reynolds number is increases from 3x 104 to 3 x 105, the coefficient of drag decrease to 0.3 at Re = 3 x 105.

(v)    For the further increase in Reynold number upto 3 x 106, The CD increases and attains a value equal to 0.7.

•    Consider an ideal fluid flowing over a stationary cylinder fo radius R, with uniform velocity U, the velocity at any point on the surface of cylinder as shown in.

Uθ= 2 U sinθ

•    Where, θ = The angular distance of the point from the forward stagnation point.

•    When the circulation Γ is imparted to the same cylinder, the flow pattern around the cylinder consists of streamlines which are series of concentric circles as shown in. The velocity at any point on the surface of the cylinder is given by.

•    The velocity at any point on the surface of the cylinder for the composite flow pattern.

Stagnation point, u = 0.

2 U sin θ = -  Γ /2πR

sin θ = - Γ/4 π U R

•    Since sinθ is negative in Equation it means θ is more than 1800 but less than 3600. The two values of θ are such that θ lies between 1800 to 2700 and other values are between 2700 to 3600.

For single stagnation point θ = 2700.

sin 2700 = Γ/4 π U R

Γ  = 4 π U R

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