A straight pipeline of internal diameter m carries oil of density kg m and dynamic…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity

Fluids and Continuum Physics, Ch Dimensional analysis, dynamical similarity and the dimensionless groups

Problem

A straight pipeline of internal diameter

D_p = 0.60

m carries oil of density

880

kg m

^{-3}

and dynamic viscosity

0.040

Pa s at a mean speed of

1.5

m s

^{-1}

. The flow is treated as steady and incompressible, and every pipe Reynolds number here is built on the internal diameter and the mean speed. ((a)) The pressure drop

\Delta p

along a length

l

of such a pipe is taken to depend on

D

l

, the mean speed

U

, the density

\rho

and the viscosity

\mu

. How many independent dimensionless groups can be formed from these six quantities? ((b)) Compute the Reynolds number of the oil flow. ((c)) The pipeline is to be modelled by a geometrically similar pipe of internal diameter

0.050

m carrying water of density

1000

kg m

^{-3}

and dynamic viscosity

1.0\times10^{-3}

Pa s. What mean water speed gives the same Reynolds number?

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