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