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  Forced vortex flow 1 Aim To understand the physics behind the flow profile of a forced vortex. 2 Objective To obtain the surface profile in a forced vortex flow. 3 Introduction In this experiment we shall generate forced vortex and understand its characteristics. Forced vortex flowis defined as a flow, in which some external torque is required to rotate the fluid mass. The fluid massin this type of flow, rotates at constant angular velocity. Examples of forced vortex are: ã  A vertical cylinder containing liquid which is rotated about its central axis with a constant angularvelocity. ã  Flow of liquid inside the impeller of centrifugal pump. ã  Flow of water through the runner of a turbine.Free vortex flow is an example of rotational flow where no external torque is required to rotate the fluidmass. Thus the liquid in case of free vortex is rotating due to the rotation which is imparted to the fluidpreviously. Some examples of free vortex flow are: ã  Flow of liquid through a hole provided at the bottom of the container. ã  Flow of liquid around a circular bend in a pipe. ã  A whirlpool in a river. ã  Flow of fluid in a centrifugal pump casing.1  Figure 1: Schematic of Experimental setup 4 Theory Under steady conditions, each particle will move with the same angular velocity and there will not beany relative motion between fluid particles. Streamlines for such a flow will be concentric circles andthe total energy is constant along a streamline but varies from one streamline to another.Using the continuity and Navier Stokes equations, derive the velocity profile and the free surface profilefor a cylindrical container of radius R, rotating with angular velocity of . Solve the problem in cylindricalcoordinates. Assume the flow to be unidirectional in nature with  v r  and  v z  to be zero. (Refer toFundamentals of Fluid Mechanics by Munson, Section 2.12.2) 5 Description The set-up consists of an open transparent acrylic cylinder, which is free to rotate about its verticalaxis. The cylinder is suitably mounted on a stainless steel plate. The plate is rotated with the helpof a variable speed motor so that cylinder rotates about its vertical axis. A pointer gauge mounted ongraduated carriage is provided with the apparatus. A proximity switch is also provided for measuringthe RPM of motor.When fluid is drawn down a plug-hole, one can observe the phenomenon of a vortex. The tangentialvelocity  v  varies inversely as the distance  r  from the center of rotation, so the angular momentum,  vr , is2  constant; the vorticity is zero everywhere (except for a singularity at the center-line) and the circulationabout a contour containing  r  = 0 has the same value everywhere. The free surface (if present) dipssharply (as  r − 2 ) as the center line is approached. 6 Utilities required 1. Electricity supply: single phase, 220 VAC, 50 Hz, 4kW. Combined with earth connection.2. Water supply.3. Floor drain required.4. Floor area required: 2.5 m  ∗  1.5 m. 7 Experimental procedure Starting Procedure: 1. Ensure that all On/Off Switches given on the Panel are at OFF position.2. Clean the apparatus and make cylinder free from dust.3. Fill the cylinder approximately  14 th with Clean Water and ensure that no foreign particles arcthere.4. Now switch ON the Main Power Supply and switch ON the motor. Then increase the speed of motor slowly.5. The cylinder is rotated at a constant speed. The free surface of the water takes the form a forcedvortex.6. After steady state conditions are achieved, surface profile readings are taken by measuring differenthorizontal distances along radius and the corresponding heights. The surface elevation at the centerof the vortex (at r= 0) is taken as the datum for all these readings7. The resulting water surface profile is recorded by traversing the pointer gauge and scale. Plot agraph between radius and height and theoretical height.8. Repeat the same procedure for different speeds of rotation. Closing Procedure: 1. Adjust DC Drive knob at ZERO.2. When experiment is over, switch off the motor first.3. Switch off Power Supply to Panel and drain water.3  8 Standard Data ã  ID of cylinder = 0.200 m ã  length of cylinder = 0.350 m ã  Acceleration due to Gravity = 9.81 m/sec2 Formulae: ã  Angular velocity:  ω  =  2 πN  60 ã  Surface Profile (derive this in the theory):  Z   =  ω 2 r 2 2 g 9 Observation table To verify symmetry of the surface profile, take surface readings at both  θ  = 0 and  θ  =  π  .Take as many r vs Z readings as possible.S.No. RPM ( ω 1 ) RPM ( ω 2 ) RPM ( ω 3 )Radial position(cm)Height(cm) Radial position(cm)Height(cm) Radial position(cm)Height(cm)12345 10 Calculations Calculation table:-RPM = , Angular velocity =S.No. Radial position (cm) Experimental surface height (cm) Theoretical Height, Z12345Plot experimental results and theoretical results for the same RPM on the same plot.Using plots verify that the flow is symmetric about the assumed axis of symmetry.Repeat this for different RPMs used in the experiment.4

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Sep 10, 2019
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