By B. Hewakandamby
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Additional resources for A First Course in Fluid Mechanics for Engineers
This has to be done considering the dominant physics associated with the phenomenon under consideration. 3 Uses of dimensional analysis Dimensional analysis is used to compare physical phenomena in various geometries. The comparison (used loosely in here) gives an indication how a system would behave. This is possible because dimensional analysis leads to similarity laws for the systems under consideration. This reduces the number of variables to consider in a given problem. com 54 A first course in Fluid Mechanics for Engineers Basics of Fluid Flow 4 Basics of Fluid Flow Introduction In the previous lecture on fluid statics we have discussed the fluid at rest.
For such analysis tracing a constant mass of fluid or a system is not practical. Therefore, a specific volume in space can be defined through which fluid can flow. Such a volume defined in space through which fluid may flow with varying mass and volume is called a control volume. Boundary of the control volume is called control surface. Control volumes could be (a) fixed in space, (b) moving volumes or (c) deforming volumes. 7a. 7b, a moving control volume can be defined around the aeroplane. To examine the flow patterns in an engine cylinder one can define a deforming control volume.
For time, velocity can be used and for the length, diameter D is used as it remains the characteristic length for the geometry. The length of the pipe could vary and could specify in terms of the diameter. 5. Forming the four pi groups ȫͳ ൌ ߩܽ ܿ ݒ ܾܦȟܲ ȫ͵ ൌ ߩܽ ܮ ܿ ݒ ܾܦ ȫʹ ൌ ߩܽ ߤ ܿ ݒ ܾ ܦ ȫͶ ൌ ߩܽ ݁ ܿ ݒ ܾ ܦ 51 ൌ ߩܽ ܿ ݒ ܾܦȟܲ ൌ ߩܽ ܮ ܿ ݒ ܾܦ A first course in Fluid Mechanics for Engineers Consider ȫͳ ൌ ߩܽ ܿ ݒ ܾ ܦȟܲ Dimensional analysis ȫʹ ൌ ߩܽ ߤ ܿ ݒ ܾܦ ܽ ܾ ܿ ܽ ܾ ܿ ȫߩ͵ ܽൌ ݁ሿ ൌ ሾܯሿͲ ሾܮሿͲ ሾܶሿͲ ሿܿ ሾߩܦܮܯെͳ ܶݒെʹ ܦܿ ݒߩܾܦȟܲ ݒൎܮሾܮܯെ͵ ሿܽ ሾܮሿܾ ሾܶܮȫെͳ Ͷ ൌ Equating the powers of each dimension, three equations can be obtained for a, b and c.
A First Course in Fluid Mechanics for Engineers by B. Hewakandamby