Description

Description:

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Related Documents

Share

Transcript

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

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks

SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...Sign Now!

We are very appreciated for your Prompt Action!

x