A First Course in Fluid Mechanics for Engineers by B. Hewakandamby

By B. Hewakandamby

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2 Buckingham’s Pi theorem Lord Rayleigh has used nondimensional groups even though a formal method of deducing them was not presented. US physicist Edgar Buckingham put forward a formal methodology to deduce all nondimensional parameters associated with a problem in 1914. It has become widely known as the Buckingham’s pi theorem since. It is called “pi” theorem after the mathematical notation π used to indicate the product of variables. In Buckingham’s pi theorem, Π is used to indicate each independent grouping of physical parameters that forms a nondimensional group.

This force acts at the pressure centre of the projected area. 16 (a), the vertical component Fy is due to the weight of the fluid held by the curved surface AE. This is the weight of the fluid volume held in AEDC. The weight of the fluid acts vertically down through the centre of gravity of AEDC. 16 (b), the force acting vertically upward is due to the liquid held by the curved surface. Should the area vertically above AE is filled with the same liquid after removing the curved surface it should be in equilibrium when the fluid is at rest.

The location of this point can be calculated by taking the moment of mass around an arbitrarily selected reference axis. 13. com 39 A first course in Fluid Mechanics for Engineers Fluid Statics When a thin plate like body is considered, the centre of mass is referred to as the centroid. The best example for such a body is a metal plate of any shape with uniform thickness. Even though the mass is evenly distributed, one can treat it as a lamina with its mass concentrated at centroid. We can easily calculate the position of the centroid for basic shapes by taking the moment around a reference axis.

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