# How to find drag of a cylinder?

How can I find a drag on the cylinder placed in uniform water flow, if I know a velocity field around it?

In the case of a potential flow, the resistance is zero (d'Alembert paradox). In the case of viscous flow, it is necessary to calculate the pressure distribution and the derivative of velocity along the normal. Calculate the integral $$F_D=\int _S{\left( \mu \frac {\partial u_t}{\partial n}n_y-pn_x\right)\mathrm dS}$$ The drag coeﬃcient is $$c_D=\frac {2F_D}{\rho U_0^2D}$$. Here $$\mu$$ is viscosity coefficient, $$\vec n=(n_x,n_y)$$ - normal vector, $$D$$ - diameter. The algorithm for solving the problem in the case of a laminar flow with the formation of Karman vortices, see on Solver for unsteady flow with the use of Mathematica FEM . Figure $$1$$ shows the velocity distribution at $$Re=100$$, the drag and lift coeﬃcients, and the pressure diﬀerence $$\Delta P$$ is deﬁned, with the front and end point of the cylinder.
Experimental data of the velocity distribution around the cylinder at $$Re=4216.8$$ @Anton Kovalyov