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2. [2 pts] Simplify the x-direction of Navier-Stokes equation for fully developed, steady state, unidirectional and in compressible pipe flow? (Be aware the NS eqn in cylindrical coordinates.) \rho\left(\frac{\partial u}{\partial

t}+u_{r} \frac{\partial u}{\partial r}+\frac{u_{\theta}}{r} \frac{\partial u}{\partial \theta}+u \frac{\partial u}{\partial x}\right)=-\frac{\partial P}{\partial x}+\rho g_{x}+\mu\left(\frac{1}{r} \frac{\partial}{\partial r}\left(r \frac{\partial u}{\partial r}\right)+\frac{1}{r^{2}} \frac{\partial^{2} u}{\partial \theta^{2}}+\frac{\partial^{2} u}{\partial x^{2}}\right)

Fig: 1

Fig: 2