1DIMENSIONAL ANALYSIS

It is a mathematical technique which makes use of study of dynamics as an artto the solution of engineering problems .

Fundamental DimensionsAll physical quantities are measured by comparison which is made with

respect to a fixed value.

Length, Mass and Time are three fixed dimensions which are of importance influid mechanics and fluid machinery. In compressible flow problems, temperature isalso considered as a fundamental dimensions.

Secondary Quantities or Derived QuantitiesSecondary quantities are derived quantities or quantities which can be

expressed in terms of two or more fundamental quantities.

Dimensional HomogeneityIn an equation if each and every term or unit has same dimensions, then it is

said to have Dimensional Homogeneity.V = u + at

m/s m/s m/s2 sLT-1 = (LT-1) + (LT-2) (T)

Uses of Dimensional Analysis1. It is used to test the dimensional homogeneity of any derived equation.2. It is used to derive equation.3. Dimensional analysis helps in planning model tests.

Dimensions of quantities1. Length LMoTo

2. Mass LoMTo

3. Time LoMoT4. Area L2MoTo

5. Volume L3MoTo

26. Velocity LMoT-1

7. Acceleration LMoT-2

8. Momentum LMT-1

9. Force LMT-2

10. Moment or Torque L2MT-2

11. Weight LMT-2

12. Mass density L-3MTo

13. Weight density L-2MT-2

14. Specific gravity LoMoTo

15. Specific volume L3M-1To

16. Volume flow rate L3MoT-1

17. Mass flow rate LoMT-1

18. Weight flow rate LMT-3

19. Work done L2MT-2

20. Energy L2MT-2

21. Power L2MT-3

22. Surface tension LoMT-2

23. Dynamic viscosity L-1M+1T-1

24. Kinematic viscosity L2MoT-1

25. Frequency LoMoT-1

26. Pressure L-1MT-2

27. Stress L-1MT-2

28. E, C, K L-1MT-2

29. Compressibility LM-1T2

30. Efficiency LoMoTo

31. Angular velocity LoMoT-1

32. Thrust LMT-2

33. Energy head (Energy/unit mass) L2MoT-234. Energy head (Energy/unit weight) LMoTo