When water is swirling, why does it take the shape of a funnel with a depression at the centre?
L. SRIHARI
Bengaluru
Before considering the problem of swirling water, say in a washbasin, it is instructive to consider a simpler related problem.
Imagine a bucket of water kept on a turntable and rotated about its vertical axis at constant speed. After the initial sloshing motion of water due to acceleration, steady state sets in and water and bucket rotate like a rigid body.
This means the rotational velocity is zero on the axis and it increases proportionately with radius, being maximum at the vertical bucket wall.
As a consequence of rotation centrifugal forces arise leading to higher pressure at the periphery. But the pressure at the free surface (water surface in contact with air), being atmospheric, is constant.
Higher pressure at radially outward locations pushes the surface up. Since the volume of water is fixed the water level comes down near the centre. This leads to a paraboloid shaped symmetric free surface with the lowest point on the axis where velocity is zero.
Now consider the present swirling water case. Here the bucket or washbasin is stationary and a swirling motion is generated by opening a drain hole. Water at the periphery is bound to have some small rotational velocities which increase when a water particle approaches the drain since angular momentum is conserved. (The usual example quoted here is that of a figure skater who spins faster by pulling her hands closer to the body.)
By Bernoulli’s principle a larger velocity leads to a lower pressure and hence the funnel shape of the free surface. If the flow rate is large the funnel shaped surface may even enter the drain. The swirling motion is more complex since it has radial and axial velocity components also unlike in the previous example. The streamlines are helical.
Similar phenomenon occurs in a tornado which is a large body of swirling air with a high velocity low pressure core. There is no free surface here and the axial motion in the core is upwards kicking up dust. If the core comes near a building it acts like a giant vacuum cleaner and can be destructive.
PROF. MOHAN D. DESHPANDE
M.S. Ramaiah School of Advanced Studies
Bengaluru
