Download Dimensional Analysis

Dimensional Analysis
1) State Buckingham’s π-theorem
2) What do you mean by: i) Geometric similarity ii) Kinematic similarity iii) Dynamic
similarity iv) Dimensional homogeneity
3) What do you mean by repeating variables? How are repeating variables selected for
dimensional analysis?
4) Define & obtain the expression for (I) Reynold’s Number (ii) Mach Number
5) Explain the terms in brief : 1) Dimensionally homogeneous equation
ii) kinematic similarity
6) Define following dimensionless numbers and state their significance:
i)froude’s number ii) Euler’s number iii) Mach’s number.
7) state Buckinghams π-theorm.why this theorem is considered over rayleighs method for
dimensional analysis
8) Briefly explain the following non-dimensional parameters:
Reynold’s number (Re)
Froude’s number (Fe)
Euler’s number (Eu)
Mach’s number (M)
9) State and derive an expression for any two dimensionless numbers
Numerical
10) The discharge Q of a centrifugal pump depends upon the mass density of fluid(Ρ) the
speed of the pump(N),the diameter of the impeller(D),the manometric head (Hm)and
viscosity of fluid(µ) ST
11) The thrust (T) of a propeller is assumed to depend on the axial velocity of the fluid (V),
the density (p) and viscosity (µ) of fluid, the rotational speed (N) rpm, and the diameter
of the propeller (D). Find the relationship for T by using dimensional analysis.
12) The force F exerted by a flowing fluid on a stationary body depends upon the length (L)
of the body, velocity (V) of the fluid, density (p) and viscosity (µ) of the fluid and
acceleration (g) due to gravity.using the dimensional analysis ST
13) state Buckingham’s π-theorm. The efficiency of a fan depends on density (p). dynamic
viscosity of the fluid µ, angular velocity w, diameter D of the rotor and the discharge Q.
express n terms of dimensionless parameters.
14) The pressure difference Δp for a viscous flow in a pipe depends upon the diameter of the
pipe ‘D’, length of pipe ‘L’, velocity of flow ‘V., viscosity of fluid µ and the density of
fluid ‘p’. Using Buckingham’s theorem, show that the relation for pressure difference p is
given
15) State Buckingham π theorem. The resistance force of a ship is a function of its length,
velocity, acceleration due to gravity and fluid properties like density and dynamic
viscosity derive the relationship in a dimensionless form.
16) Torque developed by a disc of diameter D, rotating at a speed N is dependent on fluid
viscosity ‘µ’ and fluid density ‘p’. Obtain an expression for torque,
17) Using Buckingham’s π theorem ,ST the velocity of fluid flow through a circular orifice
is given by
18) The force exerted by a flowing fluid on a stationary body depends upon the length (L) of
the body, the velocity (V) of the fluid, density (p) of the fluid, viscosity (µ) and
acceleration (g) due to gravity. Find an expression for the force using dimensional
analysis.
19) The resulting force F of a supersonic plane during flight can be considered as dependent
upon the length of the aircraft 1, velocity V, air viscosity µ, air density p and the bulk
modulus of air K. Show that
20) The shear stress (Τ) in a pipe flow depends upon the diameter of the pipe (D), velocity (v)
of the fluid, mass density (p) and dynamic visocity (µ) of the fluid and height of
roughness of projection (k) Using dimensional analysis, obtain the relation for shear
stress in a non dimensional form.
21)
22) Using the method of dimensional analysis obtain an expression for the discharge Q over a
rectangular weir The discharge depends on the head H over the wier acceleration due to
gravity g. length of weir crest L, height of the weir crest over the channel bottom Z and
the kinematic viscosity v of the liquid.
23) Derive on the basis of dimensional analysis suitable parameters to present the thrust
developed by a propeller Assume that the thrust P depends upon the angular velocity w,
speed of advance V. diameter D. dynamic viscosity µ , mass density p. elasticity of the
fluid medium which can be denoted by the speed of sound in the medium C.
24) ST the power developed in a water turbine can be expressed as: