3.3. HYDRAULIC SIMILITUDE
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In studies where skin friction drag is important, such as drag on a ship's hull, a
Froude-scaled model is operated and the total drag is measured. Skin friction drag is
analytically calculated using boundary layer theory and subtracted from the measured
total drag to give a good approximation of the form drag. The form drag is scaled to
prototype dimensions using the Froude scaling relationship, and the prototype skin
friction drag is calculated and added to the form drag to give the total drag on the
vessel.
Example 3.7. Free-Fall Terminal Velocity
Prototype
Model
Two smooth balls of equal weight but different diameters are dropped from a balloon. The larger ball has a diameter that is 3 times the diameter of the smaller ball.
Knowing that “terminal velocity" is the velocity where the drag force balances the
gravitational force, use the drag force equation (Eqn. 3.30) to determine the ratio of
larger ball terminal velocity to smaller ball terminal velocity. (Assume fully turbulent
flow conditions.)
Equating the gravitational force (fV) to the drag force (Fd) as given by the drag
force equation gives
W = CdpAV2
The prototype-to-model ratio of the above equation is
(W = CDpAV2)p
(W = CDpAV2)m
73
In studies where skin friction drag is important, such as drag on a ship's hull, a
Froude-scaled model is operated and the total drag is measured. Skin friction drag is
analytically calculated using boundary layer theory and subtracted from the measured
total drag to give a good approximation of the form drag. The form drag is scaled to
prototype dimensions using the Froude scaling relationship, and the prototype skin
friction drag is calculated and added to the form drag to give the total drag on the
vessel.
Example 3.7. Free-Fall Terminal Velocity
Prototype
Model
Two smooth balls of equal weight but different diameters are dropped from a balloon. The larger ball has a diameter that is 3 times the diameter of the smaller ball.
Knowing that “terminal velocity" is the velocity where the drag force balances the
gravitational force, use the drag force equation (Eqn. 3.30) to determine the ratio of
larger ball terminal velocity to smaller ball terminal velocity. (Assume fully turbulent
flow conditions.)
Equating the gravitational force (fV) to the drag force (Fd) as given by the drag
force equation gives
W = CdpAV2
The prototype-to-model ratio of the above equation is
(W = CDpAV2)p
(W = CDpAV2)m