School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Examples 1
These examples will help you to understand the material taught in the lectures; it is very
important that you try them be
Chapter 1: Mathematical modelling of uids
Evy Kersal
e
Introduction
Fluid dynamics (or uid mechanics) is the study of the motion of liquids, gases
and plasmas (e.g. water, air, interstellar plasma) wh
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Solutions 4
1.
Hydrostatic equilibrium.
The force on the gate is due to the pressure exerted by uids on both sides. For uids at
rest
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Solutions 2
1.
Kinematics of 2-D ows.
The scalar function u measures the rate of change of volume, hence the compressibility, of
a o
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620) Examples 5
1. Water ows in a long channel of rectangular cross-section with its bottom horizontal
except for a hump extending over s
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Solutions 3
1. If a velocity eld u is irrotational, i.e. if its vorticity = u = 0, then u = for
some velocity potential . If, in add
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Solutions 1
1.
Shear ow.
We consider a shear ow u = (u, v, w) = (ky, 0, 0) where k = 0 is a constant.
i. The position x(t) = (x(t),
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Solutions 5
1.
Critical ow past a hump.
6h0
g
U
hc
Z(x)
h(x)
Zm
V
h0
Flow rate: From mass conservation, the volume ow rate Q = u(x)h
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Examples 4
These examples will help you to understand the material taught in the lectures; it is very
important that you try them be
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Examples 3
These examples will help you to understand the material taught in the lectures; it is very
important that you try them be
School of Mathematics
University of Leeds
Fluid Dynamics (MATH2620)
Examples 2
These examples will help you to understand the material taught in the lectures; it is very
important that you try them be
FEBRUARY 1978
OLIVER, LEWELLEN'AND WILLIAMSON
301
The Interaction between Turbulent and Radiative Transport in the
Development of Fog and Low-Level Stratus
D. A. OLIVER, W. S. LEWELLEN AND G. G. WILLI