All physical quantities are expressed by magnitudes and units.
For example , the velocity and acceleration of a fluid particle are 8m/s and 10m/s2 respectively. Here the dimensions of velocity and acceleration are ms-1 and ms-2respectively.
In SI (System International) units, the primary physical quantities which are assigned base dimensions are the mass, length, time, temperature, current and luminous intensity. Of these, the first four are used in fluid mechanics and they are symbolized as M (mass), L (length), T (time), and θ (temperature).
Let us take some examples:
Shear stress is defined as force/area. Again, force = mass × acceleration
Dimensions of acceleration = Dimensions of velocity/Dimension of time.
Dimension of area = (Length)2 =L2
Hence, dimension of shear stress
Consider Newton's law for the definition of viscosity as
The dimension of velocity gradient du/dy can be written as
dimension of du/dy= dimension of u/dimension of y = (L / T)/L = T -1
The dimension of shear stress is given in Eq. (19.1).
Hence dimension of
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Dimensions of Physical Quantities
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