Consider a stationary body within the flow of some fluid. I want to calculate pressure on the surface of the body. From the Navier Stokes (incompressible, stationary, no volume forces) equations, you would get something like:(adsbygoogle = window.adsbygoogle || []).push({});

dp/dx=-rho(u du/dx+v du/dy+w du/dz)+eta(d²u/dx²+d²u/dy²+d²u/dz²)

...likewise for the other coordinates.

This means that, when calculating pressure on the surface of my body, impulse (rho(..) on the right hand side of the equation) and wall shear stress (eta(..)) come into play. That seams quite logical. But my body is not moving, so, assuming a no-slip condition for its surface, u=v=w=0, which leaves me only with shear stress.

If the body is moving and the fluid is not, you should still get the same pressure on the surface. But in this case, the first term on the right hand side of the equation (impulse) is not zero.

There must be a mistake in my reasoning. Can anybody tell me what it is?

Maybe it has something to do Euler and Lagrange?

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# Understanding Navier Stokes

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