Considering two liquids - water (viscosity 0.0013 Pa-s) and engine Oil (viscosity 1.02Pa-s) when passed at a same flow rate in a 500um channel separately, will both fluid travel at a same velocity? In other words can we apply Q = V*A to any Newtonian fluid irrespective of its viscosity?
The formula Q=V*A holds for any fluid when V is the average velocity of the fluid ( the actually velocity integrated over the cross-section A of the channel). Of course, the driving force for the flow is the pressure gradient imposed on the flow. If the flow is steady and fully developed, the pressure \Delta (P_1-P_0) over the length L of the channel will depend on the viscosity of the fluid. The more viscous the fluid, the larger the pressure drop need to obtain the same volumetric flow rate, or the same average velocity V.
The only (and short) answer to the question is yes - if you are talking about volumetric flow rate and incompressible flow: it is a direct consequence of the continuity equation.
We can go one step further, and we can even say that if both operate in the Stokes regime - ie for relatively low velocities - the velocity profile should even be exactly the same.(but not the pressure gradient).
I do not understand the last comment in the previous answer.
This is true for incompressible fluids like oil and water for the same volume flow rates. Viscosity affects the required pumping power (as a consequence of pressure drop).
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