The resisting force (F) of a supersonic plane during flight can be considered as dependent upon the length of the air craft (L), Velocity (u), air dynamic viscosity (u), air density (p), and bulk modulus of elasticity of air (ɛ). Express, by dimensional analysis, the functional relationship between these variables and the resisting force. Ans. F=(p Lu²) f (2) ), Lu p u p Note: Expressing bulk modulus of elasticity in the form of an equation &= dP dy where P is pressure, and V is volume. This mean (e) is a measure of the increment change in pressure (dP) which takes place when a volume of fluid (V) is changed by ar incremental amourt (dv). Since arise in pressure always causes a decrease in volume, i.e. (d) is always negative and so the minus sign comes in the equation to give a positive value of (ɛ). where (p) is the fluid density, (N) is speed of rotation in r.p.m, (D) is the diameter of runner, (H) is the working head, and (g) is the gravitational acceleration.