3.3. HYDRAULIC SIMILITUDE
63
role for the model engineer is to justify departures from complete similitude, and when possible, to make theoretical corrections to compensate for
lack of complete similarity (Langhaar 1951).
Munson, et al. (1990) commented that most engineering studies involve
simplifying assumptions, and it is necessary to strike a balance between
accuracy and keeping the problem simple. The degree of accuracy that
must be sought from a physical model is governed by the objective of the
study. If the model is intended to examine general trends rather than
precise details, then some variables can be neglected if they are thought
to be unimportant relative to the primary physical mechanisms involved in
the problem.
In addition, the model engineer needs to be aware of forces that are
negligible in the prototype, but which can have considerable influence in
the model. For example, surface tension and surface roughness may have
small consequence in the prototype, but they might become very significant
contributors to hydraulic processes in a very small scale model. When this
occurs, the model is said to have a scale effect.
Scale effects can also occur anytime the scale ratio of a physical parameter does not maintain the same value over the entire domain of the model.
This may result from too wide a range of flow conditions being simulated in
the model. The best guard against scale effects is to build the scale model
as large as possible. However, this tactic does not absolve the engineer from
the responsibility of examining potential scale effects.
3.3.2 Specific Hydraulic Criteria
Experience indicates that almost any major problem can be simplified into
the interplay of two major forces. This allows the similitude criteria to be
developed theoretically (Warnock 1950). Several well known criteria for
fluid flow model investigations have been developed based on the assumption that two forces dominate the flow while the other forces are minor.
Inertial forces are always present in flow problems, so inertia needs to
be balanced by one of the other forces given in Eqn. 3.6. The first step in
this development is to express each of the forces in terms of their physical
units. Thus,
F{ = mass x acceleration5 = (pL3)(V2/£) = pL^V3
5For the derivation, acceleration is taken to be a convective acceleration, such as
u^du/dx), and it is represented as V2/L. Later it will be seen that convective and
temporal accelerations are related by the Strouhal number, and this provides a familiar
relationship between V, L, and t.
Fg = mass x gravitational acceleration = pL3g
63
role for the model engineer is to justify departures from complete similitude, and when possible, to make theoretical corrections to compensate for
lack of complete similarity (Langhaar 1951).
Munson, et al. (1990) commented that most engineering studies involve
simplifying assumptions, and it is necessary to strike a balance between
accuracy and keeping the problem simple. The degree of accuracy that
must be sought from a physical model is governed by the objective of the
study. If the model is intended to examine general trends rather than
precise details, then some variables can be neglected if they are thought
to be unimportant relative to the primary physical mechanisms involved in
the problem.
In addition, the model engineer needs to be aware of forces that are
negligible in the prototype, but which can have considerable influence in
the model. For example, surface tension and surface roughness may have
small consequence in the prototype, but they might become very significant
contributors to hydraulic processes in a very small scale model. When this
occurs, the model is said to have a scale effect.
Scale effects can also occur anytime the scale ratio of a physical parameter does not maintain the same value over the entire domain of the model.
This may result from too wide a range of flow conditions being simulated in
the model. The best guard against scale effects is to build the scale model
as large as possible. However, this tactic does not absolve the engineer from
the responsibility of examining potential scale effects.
3.3.2 Specific Hydraulic Criteria
Experience indicates that almost any major problem can be simplified into
the interplay of two major forces. This allows the similitude criteria to be
developed theoretically (Warnock 1950). Several well known criteria for
fluid flow model investigations have been developed based on the assumption that two forces dominate the flow while the other forces are minor.
Inertial forces are always present in flow problems, so inertia needs to
be balanced by one of the other forces given in Eqn. 3.6. The first step in
this development is to express each of the forces in terms of their physical
units. Thus,
F{ = mass x acceleration5 = (pL3)(V2/£) = pL^V3
5For the derivation, acceleration is taken to be a convective acceleration, such as
u^du/dx), and it is represented as V2/L. Later it will be seen that convective and
temporal accelerations are related by the Strouhal number, and this provides a familiar
relationship between V, L, and t.
Fg = mass x gravitational acceleration = pL3g