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UNIT III DIMENSIONAL ANALYSIS . . . . UNIT III DIMENSIONAL ANALYSIS . The basic concepts and procedures for dimensional analysis were developed by hydraulic engineers to determine the performances of a prototype (a full-scale structure) from the data obtained by tests on a model ( a reduced-scale structure). Here we present the general method of dimensional analysis and illustrates its application to various problems of fluid machines. Some of the important principles of similarity and use of dimensionless numbers in model analysis are also studied. . . SYSTEM OF DIMENSIONS: Dimensions refer to the qualitative characteristics for physical quantities, while units are standards of comparison for quantitative measure of dimensions. The most common systems of dimensioning a physical quantity and the Mass-length-time and the Force-length-time systems referred to as the MLT and FLT systems of units. There is no direct relationship between the quantities length L, mass M and time T. These independent quantities are called fundamental quantities. In compressible fluids, one more dimension namely temperature θ is also taken as the fundamental dimension. All other quantities such as pressure, velocity and energy etc. are expressed in terms of these fundamental quantities and are called derived or secondary quantities. For example (function(){function i(e){seraph_pds.View.InitFormulas();}if(seraph_pds && seraph_pds.View)i();else document.addEventListener(‘DOMContentLoaded’,i);})()F=MLT−2:M=FT2L−1 . . Physical quantity Symbol Dimensions M-L-T System F-L-T System *Fundamental quantities . . . Mass M M FL-1T2 Length L L L Time T T T Force F MLT-2 F *Geometric quantities . . . Area A L2 L2 Volume V L3 L3 *Kinematic quantities . . . Linear velocity u,V,U LT-1 LT-1 Angular velocity ω T-1 T-1 Acceleration a LT-2 LT-2 Discharge Q,q L3 T-1 L3 T-1 Gravity g LT-2 LT-2 Kinematic viscosity ν L2 T-1 L2 T-1 *Dynamic quantities . . . Density ρ ML-3 FL-4T2 Specific Weight w ML-2T-2 FL-3 Surface tension σ MT-2 FL-1 Pressure intensity p ML-1T-2 FL-2 Modulus of elasticity E, K ML-1T-2 FL-2 Dynamic viscosity μ ML-1T-1 FL-2T Resisting force F, R MLT-2 F Thrust T MLT-2 F Torque T ML2T-2 FL Work W ML2T-2 FL Energy E ML2T-2 FL Power P ML2T-3 FLT-1 . . . . DIMENSIONAL HOMOGENEITY AND ITS APPLICATIONS: The fundamental theory of dimensional analysis is based on the following axiom: “Equations describing a physical phenomenon must dimensionally homogeneous and the units therein must be consistent”. The concept of dimensional homogeneity can be elaborated by considering the time period of oscillation…

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