A large open tank of water has its free surface m above a short horizontal outlet…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Viscous flow and dynamical similarity
Fluids and Continuum Physics, Ch Dimensional analysis, dynamical similarity and the dimensionless groups
Problem
A large open tank of water has its free surface h=2.5 m above a short horizontal outlet pipe of internal diameter d=12 mm that discharges to the atmosphere. The tank is so wide that the speed of the water at its surface is negligible. The water has density ρ=1000 kg m−3 and dynamic viscosity μ=1.0×10−3 Pa s; take g=9.8 m s−2 and atmospheric pressure to act on both the free surface and the jet.
((a)) Treating the flow along a streamline from the free surface to the pipe exit as steady, incompressible and inviscid, find the discharge speed.
((b)) Evaluate the Reynolds number of the flow in the outlet pipe, using its internal diameter, and say whether it is laminar or turbulent, taking transition near Re=2300.
((c)) In the light of (b), comment on the assumption used in (a).
((d)) If a liquid of the same density were used and discharged at the same speed, what dynamic viscosity would be needed to keep the pipe flow laminar at Re=2300?