Question

When fluid in a pipe is accelerated linearly from rest, it begins as laminar flow and then undergoes transition to turbulence at a time ttr that depends on the pipe diame- ter D, fluid acceleration a, density ρ, and viscosity μ. Arrange this into a dimensionless relation between ttr and D.

Answer 1

ttr = fcn( p, D, a, μ)

Arranged onto a relation between ttr and D:

ttr( pa^2/ μ)^1/3 = fcn[D(p^2a/ μ^2)^1/3]