13- a) The velocity of a low-speed (laminar) flow through a circular pipe changes with radius and takes the form u(r) –

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13 A The Velocity Of A Low Speed Laminar Flow Through A Circular Pipe Changes With Radius And Takes The Form U R 1 (36.4 KiB) Viewed 62 times

13- a) The velocity of a low-speed (laminar) flow through a circular pipe changes with radius and takes the form u(r) – BAP (– m2) = (1) What are the dimensions of the constant B? Also, sketch the expected shape of u(r) from -ro td ro. You can assume that B, Ap and u are all equal to 1. b) Show that the Navier-Stokes equation is dimensionally homogeneous. Here, we have ve locity components u, v, w in the spatial coordinate system I,y,z, with time t, pressure p and kinematic viscosity v =/p with dynamic viscosity and density p. ди au au au 1 др au 2 024 tu +0 + +ve at (2) д az рдах Or2 aya az2 + 2 ду