Froude Number
Def. Froude number is a dimensionless quantity that was named after scientist William Froude. Froude
number is known as the flow of inertia to the external felid. Froude number as described by William
Froude is based on speed length ratio. In fluid mechanics, the Froude number helps to know where
inertia is greater than the effects of gravity in the fluid medium. A falling jet stream is an example of a
Froude number where a jet cylinder is accelerated under the presence of gravity.
It describes different flow regimes of open channel flow. The Froude number is a ratio of inertial and
gravitational forces.
· Gravity (numerator) - moves water downhill
· Inertia (denominator) - reflects its willingness to do so.
Significance & Importance: The Froude number is a measurement of bulk flow characteristics such as
waves, sand bedforms, flow/depth interactions at a cross section or between boulders.
Being a dimensionless quantity Froude number is used in the comparison. It measures the comparison
of waves which makes resistance between bodies of various sizes and shapes.
The denominator represents the speed of a small wave on the water surface relative to the speed of the
water, called wave celerity. At critical flow celerity equals flow velocity. Any disturbance to the surface
will remain stationary. In subcritical flow the flow is controlled from a downstream point and
information is transmitted upstream. This condition leads to backwater effects. Supercritical flow is
controlled upstream and disturbances are transmitted downstream.
Wave propagation can be used to illustrate these flow states: A stick placed in the water will create a V
pattern of waves downstream. If flow is subcritical waves will appear in front of the stick. If flow is at
critical waves will have a 45 0 angle. If flow is supercritical no upstream waves will appear and the wave
angle will be less than 450.
Applications:
1. Ship Hydrodynamics: In the applications of marine hydrodynamics, Froude number is usually referred
to as Fn,
Here, u is considered as the relative flow velocity in between the sea and ship, g is the acceleration due
to gravity and L is the length of the ship at the level of the waterline, it is also denoted as Lwl. It is the
important parameter that is calculated for the resistance or ship drag in respect to the wave-making
resistance.
In the planning crafts, while the waterline length is too speed-dependent, the Froude number can be
defined as displacement Froude number, and thus the reference length is taken from the volumetric
displacement of the hull, it is represented as:
2. Wind Engineering: In dynamically sensitive structures, considering the wind effects is necessary for
the simulation of the combined effect of the vibrating mass along with the fluctuating force of the wind.
When simulating the hot smoke plumes when combined with the natural wind, the scaling of the Froude
number is necessary for the maintenance of the correct balance between the buoyancy forces and the
momentum of the wind.
3. Shallow Water Waves: The shallow waterways such as hydraulic jumps and tsunamis, U is considered
as the average flow velocity, where this U is averaged to the cross-section that is perpendicular to the
flow direction. Thus the wave velocity c is defined as:
