Dimensional analysis can be used in problems other than áuid mechanics ones. The important variablesaffecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beamlength `, area moment of inertia I, modulus of elasticity E, material density , and Poissonís ratio , so thatT = f cn(`; I; E; ; )Recall that the modulus of elasticity has typical units of N/m2 and Poissonís ratio is dimensionless.(a) Find dimensionless version of the functional relationship.(b) If E and I must always appear together (meaning that EI is e§ectively a single variable), Önd a dimensionless version of the functional relationship. Dimensional analysis can be used in problems other than fluid mechanics ones. The important variablesaffecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beamlength , area moment of inertia I, modulus of elasticity E, material density p, and Poisson's ratio o, so thatT= fen(l, I, E, p,o)Recall that the modulus of elasticity has typical units of N/m² and Poisson's ratio is dimensionless.(a) Find dimensionless version of the functional relationship.(b) If E and I must always appear together (meaning that EI is effectively a single variable), find a dimen-sionless version of the functional relationship.

Dimensional analysis can be used in problems other than fluid mechanics ones. The important variables affecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beam length é, area moment of inertia I, modulus of elasticity E, material density p, and Poisson's ratio , so that T = fen(l,I,E,p.a)

Dimensional analysis can be used in problems other than fluid mechanics ones. The important variables affecting the period of a vibrating beam (usually designated as T and with dimensions of time) are the beam length é, area moment of inertia I, modulus of elasticity E, material density p, and Poisson's ratio , so that T = fen(l,I,E,p.a)

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.13P: 5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its...

See similar textbooks

Similar questions

5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
Dimensional analysis is to be used to correlate data on bubble size with the properties of the liquid when gas bubbles are formed by a gas issuing from a small orifice below the liquid surface. Assume that the significant variables are bubble diameter D, orifice diameter d, liquid density rho, surface tension sigma (in N/m), liquid viscosity mu, and g. Select d, rho, and g as the core variables.
The thrust force of propeller (P) depends upon the flow velocity V, angular velocity o, diameter D, dynamic viscosity , density p. the speed of sound in the medium C. (1) Derive the relationship between the above variables and the thrust force by using Buckingham's IT-theorem. (2) Explain the physical meaning of the obtained dimensionless groups. إجابت
During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumed that the energy released E, was a function of blastwave radius R, air density ρ, and time t. Arrange these variables into single dimensionless group, which we mayterm the blast wave number.
The radius R of a mushroom cloud generated by a nuclear bomb grows in time. We expect that R is a function of time t, initial energy of the explosion E, and average air density ? . Use dimensional analysis to express the relationship between R, t, E, and ? in dimensionless form.
The force, F, acting on a billboard due to wind depends on it length, l, height, h, the modulus of elasticity of the board, E, and the specific weight, γa, of the air. Using dimensional analysis, find an appropriate dimensionless relationship.
Independent variables in a turbomachine are the impeller diameter, D, angular speed, ω, and fluid viscosity and density. Dependent properties are volumetric flow rate, Q, head, H (energy per unit mass), and power input, P. Use ρ, ω, and D as repeating variables in a dimensional analysis. a) Determine the dimensionless ratios that characterize this problem. b) Under what conditions will flows in two different machines be similar? c) Determine the speed of operation for machine 2 for the same flow as machine 1 if D2/D1 = 2 and viscous effects are unimportant. What will be the head ratio under these conditions? Note:hand written solution should be avoided.
During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to estimate theenergy released by an atomic bomb explosion. He assumedthat the energy released E , was a function of blast waveradius R , air density ρ, and time t . Arrange these variablesinto a single dimensionless group, which we may term theblast wave number .
The thrust F of a propeller is generally thought to be afunction of its diameter D and angular velocity V , the forwardspeed V , and the density ρ and viscosity μ of the fl uid.Rewrite this relationship as a dimensionless function.
The time t d to drain a liquid from a hole in the bottom of atank is a function of the hole diameter d , the initial fluidvolume y 0 , the initial liquid depth h 0 , and the density ρ andviscosity μ of the fluid. Rewrite this relation as a dimensionlessfunction, using Ipsen’s method.
The power P generated by a certain windmill design dependson its diameter D , the air density ρ , the wind velocity V , therotation rate Ω , and the number of blades n . ( a ) Write this relationship in dimensionless form. A model windmill, of diameter50 cm, develops 2.7 kW at sea level when V = 40 m/s andwhen rotating at 4800 r/min. ( b ) What power will be developedby a geometrically and dynamically similar prototype, ofdiameter 5 m, in winds of 12 m/s at 2000 m standard altitude?( c ) What is the appropriate rotation rate of the prototype?
Determine the form of an equation for the distance (s) that a sphere will fall in time t, if it starts with an initial velocity and the resistance of the fluid through which it falls is taken into consideration. Resistance is dependent upon the density (ρ) and viscosity (μ) of the medium and the diameter (d) and mass (m) of the sphere. Hence in addition to g, v and t these factors are incorporated. S = f (g, v, t, m, d, ρ, μ) USE DIMENSIONAL ANALYSIS AND BUCKINGHAM PI THEOREM