## Drag On A Cylinder

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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 10

(iv) When Reynolds number is increases from 3x 10

(v) For the further increase in Reynold number upto 3 x 10

• 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.

U

• 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 180

For single stagnation point θ = 270

sin 270

Γ = 4 π U R

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(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 10

^{4}, the coefficient of drag increases and attains maximum value C_{D}= 1.2 at R_{e }= 3x10^{4}.(iv) When Reynolds number is increases from 3x 10

^{4}to 3 x 10^{5}, the coefficient of drag decrease to 0.3 at R_{e}= 3 x 10^{5}.(v) For the further increase in Reynold number upto 3 x 10

^{6}, The C_{D}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.

U

_{θ}= 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 180

^{0}but less than 360^{0}. The two values of θ are such that θ lies between 180^{0}to 270^{0}and other values are between 270^{0}to 360^{0}.For single stagnation point θ = 270

^{0}.sin 270

^{0}= Γ/4 π U RΓ = 4 π U R

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