Consider a solid cylinder of circular cross-section which travels at constant velocity U normal to its axis through a fluid of very vast extent. That is, it is presumed that the linear dimensions of the fluid are many orders of magnitude greater than the diameter of the cylinder. The flow of fluid induced by the motion of the cylinder can be expected to be essentially two-dimensional, considering that the cylinder is very long compared with its diameter. This implies that the picturre of flow is the same in any plane which is normal to the axis of the cylinder.
If the flow is presumed to be Laplacian (i.e. divergenceless and irrotational) then we can evaluate the pattern of flow by the methods outlined in Art. 1.11, making use of the appropriate boundary conditions. It is sufficient to state at this point that Laplacian flow adjacent to the cylinder is a rather idealized type of motion, however it does possess certain characteristics which warrant its investigation. Practically speaking, the flow would exist immediately after an impulse is imparted to a cylinder which was originally at rest in a static fluid.
The boundary condition to be satisfied is Eq. (228). We will take the origin of the reference frame at the center of the cylinder, and thus refer
all quantities relative to the moving cylinder. The normal component of the fluid velocity to the surface is
See Fig. 1.13-1 for details. Since the flow is presumed to
be Laplacian, it follows that 
can be expressed
as
Consequently, Eq. (224) can be written as
The transform 
, which is capable of satisfying
condition (234a), is
which implies that
Applying condition (234a) gives
which can be satisfied only if
The velocity at distance r is
or
In order to select the proper sign of n in Eq (238a) we introduce
a second condition which is simply that the motion is to be confined
to the neighborhood of the cylinder; that is, the fluid is not
significantly disturbed at a great distance from the cylinder.
This requires that we take 
and, consequently,
The streamlines and isolines of velocity potential repesented by Eqs. (240a,b) are shown in Fig. 1.13-2. The families of isolines are circles which pass through the point 0 if extended inside the cylinder.
It is of interest to compute the kinetic energy of the fluid motion induced by the passage of the cylinder through the fluid. This is given by the integral
where 
is the mass density of the fluid, presumed constant,
and 
is the total kinetic energy of that fluid contained
between two planes of unit distance apart and normal to the
axis of the cylinder and extending indefinitely in the x
and y directions. If we carry out the integration, making use
of Eq. (240c), we find that
or
where 
represents the mass of fluid displaced
by the cylinder per unit length of cylinder.
If the cylinder is accelerated, then a force commensurate with the mass of the cylinder plus the mass M' is required to produce the given acceleration. That is, of the kinetic energy being supplied to the cylinder, some is used to accelerate the cylinder and some is used to accelerate the water in the neighborhood of the cylinder. The effective mass of the cylinder in the fluid therefore includes the mass M'.