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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.

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
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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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