Water ( ) in a laboratory tank forms a Rankine vortex: solid-body rotation at out to…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Kinematics, conservation laws and ideal flow
Fluid Dynamics, Ch Euler's equation in Lamb's form and the four Bernoulli theorems
Problem
Water (ρ=998kgm−3) in a laboratory tank forms a Rankine vortex: solid-body rotation at Ω=15rads−1 out to a core radius Rc=0.08m, and irrotational swirl outside. The flow is steady.
((a)) Use Lamb's form of Euler's equation to find how much the Bernoulli function B rises between the axis and the edge of the core.
((b)) State, giving the theorem used, what happens to B for r>Rc.