# The use of temperature as a variable in hydraulics

El Agib, Ahmed A.R (1965) The use of temperature as a variable in hydraulics. PhD thesis, University of Glasgow.

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## Abstract

Use of Bernoulli (or Euler) equation in Hydraulics is restricted to flows which can be considered frictionless and in which there is no external work transfer. Flow of a liquid causes changes in the thermodynamic state of the liquid - these changes being inevitably irreversible. It is clear therefore that a complete description of liquid flow processes can only be obtained by using the more general equations of thermodynamics. The main obstacle to this procedure has been the difficulty of measuring the small temperature differences encountered in liquid flow and on which the thermodynamic equations are dependent. Thus research was aimed first at developing simple methods and techniques for measuring small temperature differences such as those occurring in hydraulic (or liquid) flow systems; and at surmounting the various difficulties inherent in such measurements. As a result it is now in most cases possible to obtain an accuracy of +/- 1mC° in the measurement of temperature difference across a hydraulic flow system (l millidegree = 0.001 C°). Under favourable conditions an accuracy of +/- 0.3m C° has been attained. The apparatus used for such measurements is cheap and very simple. A suitable equation for use in the thermodynamic treatment of liquid flow is the Steady Flow Energy Equation, It was found necessary, however, to recast this equation in a special form for convenient application to liquid flow. This necessitated introduction of certain thermodynamic properties (e.g. ∂h/∂P)T). The values of these properties for water were evaluated and presented in tabular form for the ranges 1-50°G and 1-200 atmospheres. Examples of the order of magnitude of these properties for some other common liquids are also shown. In contrast to Bernoulli and Euler equations this version of the Steady Flow Energy Equation depends on both the temperature and pressure as variables. The equation has been used in the analysis of a number of hydraulic flow systems of varied nature with very satisfactory results. Research was conducted to show the practicability and advantages of using the temperature as a variable in two important fields of hydraulic practice, namely the measurement of efficiency and of the rate of flow. The development of the techniques of temperature measurement - referred to above - rendered practicable the application of the thermodynamic methods of measuring hydraulic efficiency to machines operating at heads as low as 100 feet - lower than hitherto possible. The development of these techniques of thermometry also rendered practicable the use of novel and simple thermometric methods for measuring the rate of flow. In conclusion it is hoped that the satisfactory results obtained in this research will help to inspire more confidence in the use of temperature as a variable in Hydraulics and stimulate interest in Thermohydraulics - the thermodynamic treatment of liquid flow.

Item Type: Thesis (PhD) Doctoral Adviser: A S Thomson Hydraulic engineering, Thermodynamics, Fluid mechanics 1965 Enlighten Team glathesis:1965-73070 Copyright of this thesis is held by the author. 14 Jun 2019 08:56 14 Jun 2019 08:56 http://theses.gla.ac.uk/id/eprint/73070