Question

Q1. The velocity v of a fluid beyond which streamline flows, ceases and turbulence begins depending on the radius r of the tube, density p and viscosity n of the fluid. Using dimensions (dimensional analysis), obtain an expression which relates v. r, p and n. Hint: v « rpn => y = krapne mass volume distance force Velocity density viscosity time (area) [velocity gradient] velocity gradient velocity Using dimensional analysis, find the values of a, b and c. length

Answer 1

The coefficient K is a dimensionless number called as Reynolds number which can be used to determine the nature of flow in pressure pipes as well as in open channels. It tells us whether the flow is laminar or turbulent.

is vo OY where K is a dimensionless Coefficient. Using M-L-T system, the corresponding equation for dimensions is: The dimension of R, being a constant, is taken as may be premised that the functional relationship f ( les fon) k raghna IMPL'T-'] = [0147" M-ML-*--) VER Force = MLTY unity { viscosity = (area) (velocity gradient) {Density = Volume MLT-2 L.MT-1 ML-3. Y mass M L3 M: 3 Ti -C or → For dimensional homogeneity, exponents of M, L and I are equated om both sides, the equations are: 0 = b + c ; I = a-36-C ; -1 C = 1l, using in equations we have b+1 ) b = -1 from equation , we have 1 = 0 - 3(-1)-1 1= a +3-1 =) [a=-1 V = Ke-f-in' i K= Sve this is the required 0 = is we get n Relatinship CS Scanned with CamScanner