1. SOURCE FLOW – SINK FLOW - VORTEX FLOW DEPARTMENT OF CIVIL ENGINEERING BE – II SEMESTER - III

2. PREPARED BY NAMEENROLLMENT NO MARGI DAVE 130420106012 DIPIKA CHAUDHARI 130420106009 PRASHANT CHOTALIYA 130420106011 CHETAN CHAUHAN 130420106010

3. Types of fluid motion Fluid Motion Rectilinear Motion Radial Motion or Radial Flow Radially outward or Source Flow Radially inward or Sink Flow Rotary or Vortex Motion Free vortex Forced Vortex

4. RADIAL FLOW  Radial flow is defined as that type of flow in which the fluid flows in radial direction in such a way that pressure and velocity at any point changes with respect to distance of that point from the central axis only.

5. SOURCE FLOW  The source flow is the flow coming from a point(source) and moving radially in all directions of a plane at uniform rate.

6.  The figure shows a source flow in which the point O is the source from which the fluid moves radially outward.  The strength of a source is defind as the volume flow rate per unit depth. The unit of strength of source is m 2 /s.  It is represented by q. o u r = q/2πr Where u r = radial velocity of flow at a radius r from the source O q = volume flow rate per unit length r = radius

7. SINK FLOW  The sink flow is the flow in which fluid moves radially inwards towards the point where it disappears at constant rate.  The pattern of stream lines and equipotential lines of a sink flow is the same as that of source flow.  The equation for the sink flow is same as that of source flow except that in sink flow equation, q is replaced by (-q).

9. ROTARY OR VORTEX MOTION  A mass of fluid in rotation about a fixed axis is called vortex.  The rotary motion of fluid is also called vortex motion.  In this case the rotating fluid particles have velocity in tangential direction.  Thus the vortex motion is defined as motion in which the whole fluid mass rotates about an axis.  The vortex motion is of two types (i) Free vortex (ii) Forced vortex

10. FREE VORTEX FLOW  Free vortex flow is that type of flow in which the fluid mass rotates without any external impressed contact force.  The whole mass rotates either due to fluid pressure itself or the gravity or due to rotation previously imparted. Energy is not expended to any outside source.  The free vortex motion is also called Potential voetex or Irrotational vortex. The relation between velocity and radius is obtained by putting the value of external torque zero or time rate of change of angular momentum zero. ∂ (mvr)/∂t = 0 vr = constant ∂ (mvr)/∂t = 0 vr = constant

11. Examples of Free Vortex flow Whirlpool in river. Rotary flow observed in wash basin while draining the liquid through the outlet at bottom. Some instances of a vortex include a ring of smoke, drag from the wing of an aircraft, a tornado, dust devil or waterspout, hurricanes, sunspots on the Sun, black holes, and spiral galaxies, such as our own Milky Way.

12. FORCED VORTEX MOTION  Forced vortex motion is one in which the fluid mass is made to rotate by means of some external agencies.  The external agency is generally the mechanical power which imparts the constant torque on the fluid mass.  The forced vortex motion is also called flywheel vortex or rotational vortex. The fluid mass in this type of flow, rotates at constant angular velocity w. The tangential velocity is given by v = w x r

13. Examples of Forced Vortex flow Flow of liquid inside the impeller of a centrifugal pump and inside the runner of hydraulic turbine.

14. v r = constant v α (1/r) v r = constant v α (1/r) v = w x r

16. Explanation of the experiment  Let us create two basic types of vortices.  Connect two plastic bottles and poke a hole through the cap. Fill water in the lower bottle.  When you turn the bottles upside down and rotate, a vortex is formed in the water. (If the water does not start flowing, give a quick squeeze to the top bottle to get it going.)  The vortex formed in this case is called a “free vortex.” This is the vortex formed when draining a bathtub or a sink. The speed is faster as you get closer to the center; that is, the peripheral speed is inversely proportional to the radius.  In contrast, the vortex seen in a water bottle fixed to the center of a turntable is called a “forced vortex.” The peripheral speed is faster as you move away from the center; it is proportional to the radius. The water moves together with the container and will not deform. The water behaves like a rotating solid.

18. REFERENCES  Hydraulics And Fluid Mechanics by Dr. Jagdish Lal  Fluid Mechanics And Hydraulic Machines by Dr. R.K. Bansal  www.redorbit.com www.redorbit.com  www.mdp.eng.cam.ac.ukwww.mdp.eng.cam.ac.uk  www.google.com