Q1) The vertical displacement h of a freely falling body from its point of projection at any time 1, is determined by the acceleration due to gravity g. Find the relationship of h with / and g using Buckingham's Pi theorem.

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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Q1)
The vertical displacement h of a freely falling body from its point of projection at any
time t, is determined by the acceleration due to gravity g. Find the relationship of h
with / and gusing Buckingham's Pi theorem.
Q2)
For a steady, fully developed laminar flow through a duct, the pressure drop per unit
length of the duct A pll is constant in the direction of flow and depends on the
average flow velocity V, the hydraulic diameter of the duct D, the density p, and the
viscosity u, of the fluid. Find out the pertinent dimensionless groups goveming the
problem by the use of Buckingham's a theorem.
Q3)
Drag force F, on a high speed air craft depends on the velocity of flight V, the
characteristic geometrical dimension of the air craft 1, the density p, viscosity u, and
isentropic bulk modulus of elasticity E,, of ambient air. Using Buckingham's n
theorem, find out the independent dimensionless quantities which describe the
phenomenon of drag on the aircraft.
Transcribed Image Text:Q1) The vertical displacement h of a freely falling body from its point of projection at any time t, is determined by the acceleration due to gravity g. Find the relationship of h with / and gusing Buckingham's Pi theorem. Q2) For a steady, fully developed laminar flow through a duct, the pressure drop per unit length of the duct A pll is constant in the direction of flow and depends on the average flow velocity V, the hydraulic diameter of the duct D, the density p, and the viscosity u, of the fluid. Find out the pertinent dimensionless groups goveming the problem by the use of Buckingham's a theorem. Q3) Drag force F, on a high speed air craft depends on the velocity of flight V, the characteristic geometrical dimension of the air craft 1, the density p, viscosity u, and isentropic bulk modulus of elasticity E,, of ambient air. Using Buckingham's n theorem, find out the independent dimensionless quantities which describe the phenomenon of drag on the aircraft.
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