Example: The pressure difference (Ap) between two point in a pipe due to turbulent flowdepends on the velocity (V), diameter (D), dynamic viscosity (µ), density (p), roughnesssize (e), and distance between the points (L). using dimensional analysis determine thegeneral form of the expression (use MLT system).

Example: The pressure difference (Ap) between two point in a pipe due to turbulent flow depends on the velocity (V), diameter (D), dynamic viscosity (μ), density (p), roughness size (e), and distance between the points (L). using dimensional analysis determine the general form of the expression (use MLT system).

Example: The pressure difference (Ap) between two point in a pipe due to turbulent flow depends on the velocity (V), diameter (D), dynamic viscosity (μ), density (p), roughness size (e), and distance between the points (L). using dimensional analysis determine the general form of the expression (use MLT system).

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 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

See similar textbooks

Similar questions

When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the weight of the sphere is balanced by the buoyant force and the frictional resistance of the fluid. Make a dimensional analysis of this problem and indicate how experimental data for this problem could be correlated. Neglect compressibility effects and the influence of surface roughness.
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.
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.
Evaluate the use of dimensionless analysis using the Buckingham Pi Theorem for a given fluid flow system (D4) , where resistance tomotion ‘R’ for a sphere of diameter ‘D’ moving at constant velocity on the surface of a liquid is due to the density ‘ρ’ and the surfacewaves produced by the acceleration of gravity ‘g’. The dimensionless quantity linking these quantities is Ne= Function (Fr). To do thisyou must apply dimensional analysis to fluid flow system given in Figure 1 (P11). PICTURE IS ALSO ATTACHED
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
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 volume flow Q through an orifice plate is a function ofpipe diameter D , pressure drop D p across the orifice, fluiddensity ρ and viscosity μ , and orifice diameter d . Using D ,ρ , and ∆ p as r e peating variables, express this relationshipin dimensionless form.
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 speed of sound c in an ideal gas is known to be a function of absolute temperature T, universal ideal gas constant Ru, molar mass (molecular weight) M of the gas, and ratio of specific heats k. Showing all your work, use dimensional analysis to find the functional relationship between these parameters.
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 speed of sound c in an ideal gas is known to be a function of the ratio of specific heats k, absolute temperature T, and specific ideal gas constant Rgas. Showing all your work, use dimensional analysis to find the functional relationship between these parameters.
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.