# 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? ## 1 Answer

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 • Oh, I see, is it from the stress constitutive equation? I heard of the momentum method, that is related to the momentum deficit of flow behind the cylinder in the wake region. I just dont understand how far from the cylinder should I compute the integral? – Anton Kovalyov Apr 21 at 13:05
• Do you assume that the flow is turbulent? – Alex Trounev Apr 21 at 14:01
• Tbh, I don't really know, I looked it up on NASA and it seems to be Unsteady- Oscillating. My Re = 4200 . And it does look like the picture you sent – Anton Kovalyov Apr 21 at 14:27
• I am writing code for this case now. Formulate the problem more accurately and give a link to the NASA page. – Alex Trounev Apr 21 at 14:43
• I can give you an access to a data set I have from the experiment docs.google.com/spreadsheets/d/… – Anton Kovalyov Apr 21 at 14:47