explanation and methord of using renolds theorm

2. DIVAKAR SINGH (1641018130)
RUDRA RATH (1641018139)
NISHANT SINGH (1641018182)
GANESH SAHU (1641018323)
GROUP MATE’S:-

3.  The theorem is named after Osborne Reynolds (1842–1912). It is
used to recast derivatives of integrated quantities and is useful
in formulating the basic equations of continuum mechanics.
 Consider integrating f = f(x,t) over the time-dependent
region Ω(t) that has boundary ∂Ω(t), then taking the derivative
with respect to time
 If we wish to move the derivative within the integral, there are
two issues: the time dependence of f, and the introduction of
and removal of space from Ω due to its dynamic boundary.
Reynolds' transport theorem provides the necessary
framework.
INTRODUCTION

4.  Reynolds' transport theorem can be derived as:
In which n(x,t) is the outward-pointing unit normal
vector, x is a point in the region and is the variable of
integration, dV and dA are volume and surface elements at x,
and vb(x,t) is the velocity of the area element – so not
necessarily the flow velocity. The function f may be tensor-,
vector- or scalar-valued. Note that the integral on the left
hand side is a function solely of time, and so the total
derivative has been used.
GENERAL
PRINCIPLE:-

5.  Experiments confirm that, after a certain length of
flow, a laminar boundary layer will become unstable
and turbulent. This instability occurs across different
scales and with different fluids, usually
when Rex ≈ 5×105.
 laminar flow occurs when ReD < 2000 and turbulent
flow occurs when ReD > 4000. In the interval between
2000 and 4000 it flows with uniformity.
LAMINAR-TURBULENT
TRANSITION

6.  10L WATER CONTAINER
 1 M LONG TRANSPERENT PIPE.
 VALVE
 DIE
 CONTAINER CONTAINING DIE(SYRINGE USED)
 OUTLET PIPE
MATERIAL REQUIRED

7. STEPS OF REYNOLDS
EXPERIMENT

8. STEPS OF REYNOLDS
EXPERIMENT

9. STEPS OF REYNOLDS
EXPERIMENT

10. STEPS OF REYNOLDS
EXPERIMENT

11. STEPS OF REYNOLDS
EXPERIMENT

12. STEPS OF REYNOLDS
EXPERIMENT

13. GROUP-11
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