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For Duct Continuity: \frac{\partial v}{\partial y}=0 Momentum: \rho g_y-\frac{\partial p}{\partial y}+\mu\left(\frac{\partial^2v}{\partial x^2}+\frac{\partial^2v}{\partial y^2}\right)=0 For Circular Pipe: Continuity: \frac{\partial}{\partial r}(v_z)=0 Momentum...

How could I calculate the volumetric flow of a fluid due to the weight of a piston in a cylinder? At first moment i I thought the Hagen-Poiseuille equation, but I'm not sure. Any suggestions?

I think this equation might solve your problem. \frac{dE}{dt}=\dot{Q}-\dot{W}+\overbrace{\sum_{i}\dot{m_i}\left(h_i+\frac{v_{i}^{2}}{2}+z_i \right)}^{Inlet flow}-\overbrace{\sum_{j}\dot{m_j}\left(h_j+\frac{v_{j}^{2}}{2}+z_j \right)}^{Outlet flow}

The other i got \frac{\partial \omega}{\partial t}=\frac{\mu}{\rho}\nabla \times (\nabla^2 V) What now?

Can i assume if div(V)=0 then it's a steady flow problem?

\nabla p=\rho g + \mu \nabla^2 V-\rho\frac{\partial V}{\partial t} \nabla^2 p=\nabla .(\rho g) + \mu\nabla . (\nabla^2 V)-\rho\nabla . \left(\frac{\partial V}{\partial t}\right) \nabla^2 p=\nabla .(\rho g) + \mu\nabla^2(\nabla V)-\rho\nabla . \left(\frac{\partial V}{\partial t}\right)...

I really confused... There are a lot of terms in dV/dT and gravity that become 0, but in vicosity how could i do?

i tried but it not looks simple to do

Can somobody help me how to get the 2.72 and 2.73 equation?? http://imageshack.com/a/img89/5594/kiw6.jpg

Show them your results! They can't argue with facts! Or they have been a bunch of ... with you

Easy solution. Buy a Thermo-Hygrometer and measure your room!

This is not a general solution. Only works because the air outside is cooler.

You're right! Because you're softening the heat with airflow!

When you have a heat source like your body, computer, sun, etc you have to have airflow to romeve it. The complete equalization of a system occurs when you don't have any heat source. Look at the equation what happen when w=0 ?

Without airflow it's impossible to expect your room be cooler because the convection has a higher efficiency to remove heat than conduction. It's impossible to doesn't have airflow due to the buoyancy force and other factors. Keeping your window open will help this situation but it's very hard...