CIVE 1400 FLUID MECHANICS EFM iETSI School of 一1400流体学 EFM ietsi学院.docVIP

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CIVE 1400 FLUID MECHANICS EFM iETSI School of 一1400流体学 EFM ietsi学院.doc

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CIVE 1400 FLUID MECHANICS EFM iETSI School of 一1400流体学 EFM ietsi学院

CIVE 1400: FLUID MECHANICS Examination May/June 1996 Model answers. 1(a) State Buckingham’s ? Theorems and explain the uses of dimensional analysis. (8 marks) 1(b) An apparatus is used to measure the pressure drop in a pipe of 3cm diameter in which water is flowing at 1.1 m/s. Use Buckingham’s ? Theorems to calculate the velocity of air in a 2 cm diameter pipe which will give kinematically similar conditions. If the pressure drop over a certain length of pipe bearing water is 1 kN/m2, what is the equivalent pressure drop in the pipe bearing air? For water kinematic viscosity was 1.31 ( 10-6 m2/s and the density 1000 kg/m3. For air those quantities were 15.1 ( 10-6 m2/s and 1.19 kg/m3. (12 marks) 1(a): There are two theorems accredited to Buckingham, and know as his ? theorems. 1st ? theorem: A relationship between m variables (physical properties such as velocity, density etc.) can be expressed as a relationship between m-n non-dimensional groups of variables (called ? groups), where n is the number of fundamental dimensions (such as mass, length and time) required to express the variables. 2nd ? theorem Each ? group is a function of n governing or repeating variables plus one of the remaining variables. In engineering the application of fluid mechanics in designs make much of the use of empirical results from a lot of experiments. This data is often difficult to present in a readable form. Even from graphs it may be difficult to interpret. Dimensional analysis, for which the Buckingham ? theorems give a good strategy to perform, provides a method for choosing relevant data and how it should be presented. If it is possible to identify the factors involved in a physical situation, dimensional analysis can form a relationship between them. Often hydraulic structures are too complex for simple mathematical analysis and a hydraulic model is build. Usually the model is less than full size but it may be greater. The real structure is known as the prototype. Measurements