Section A
Q1.
(a) The water flows steadily through a pipe of length L and radius R = 75 mm. The velocity distribution across the outlet is given by (u)/(U_{\textmax}) = 1 - (r3)/(R3) The value of U_{\textmax} = 3 m/s. The inlet velocity is uniform and expressed as U. Find the net rate of volumetric flow out from the outlet control surface (m3/s) and the value of U (m/s).
(b) Two immiscible, incompressible liquids are flowing in the z-direction (Refer Figure) in a horizontal thin slit of length L and width W under the influence of a pressure gradient (po-pL) / L). The fluid flow rates are adjusted so that the slit is half filled with fluid I (the denser phase) and half filled with fluid II (the less dense phase). The fluids are flowing sufficiently slow that no instabilities occur and the interface remains exactly planar. The velocity variation for the fluid II is given by vz^{\textII} = ((p0 - pL) b2)/(2 μ^{\textII} \cdot L) (2 μ^{\textII})/(μ^{\textI} + μ^{\textII}) ) + (μ^{\textI} - μ^{\textII})/(μ^{\textI} + μ^{\textII}) ) (x)/(b) ) - (x)/(b) )2 Find the value of (x)/(b)) at the plane of zero shear stress for μ^I = 3 μII.
