Please answer all what is asked, aligned with honor code. Dimensional analysis with Buckinham's Pi Theorem is applied to the relationship between frictional head loss, H7, and other variables in a horizontal pipe of circular cross-section, such as pressure dropdiameter D., thedrdensity of the fluid p, viscosity u and the mean velocity of the fluid v. The dimension balance for these variables is [H¡] = [1°[DPH'vf.What are algebraic equations for the powers of the dimensions [M], [L], [T]?(e.g., [M]: 3=a+2*b; Write only the bold part in the available sections.)[M] :[L) :[T] :

given; head lossHf=dpdxaDbρcμdvf

Dimensional analysis with Buckinham's Pi Theorem is applied to the relationship between frictional head loss, H7, and other variables in a horizontal pipe of circular cross-section, such as pressure drop . diameter D, the density of the fluid p, viscosity u and the mean velocity of the fluid v. The dimension balance for these variables is [H;]= [ D]le]°[µ]*lv]F. What are algebraic equations for the powers of the dimensions [M], [L], [T]? (e.g. [M]: 3=a+2*b; Write only the bold part in the available sections.) [M] : [L) :

Dimensional analysis with Buckinham's Pi Theorem is applied to the relationship between frictional head loss, H7, and other variables in a horizontal pipe of circular cross-section, such as pressure drop . diameter D, the density of the fluid p, viscosity u and the mean velocity of the fluid v. The dimension balance for these variables is [H;]= [ D]le]°[µ]lv]F. What are algebraic equations for the powers of the dimensions [M], [L], [T]? (e.g. [M]: 3=a+2b; Write only the bold part in the available sections.) [M] : [L) :

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.
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.
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
At a sudden contraction in a pipe the diameter changes from D, to D2. The pressure drop, Ap, which develops across the con- traction is a function of D, and Dz, as well as the velocity, V, in the larger pipe, and the fluid density, p, and viscosity, u. Use D, V, and u as repeating variables to determine a suitable set of dimensionless parameters. Why would ti be incorrect to include the velocity in the smaller pipe a sa nadditional variable?
There are many common dimensionless numbers used to describedifferent physical effects. Such dimensionless numbers are usually a ratioof specific properties, for example, the Reynolds number represents theratio of inertial to viscous forces.Choose three of the following dimensionless numbers and describe whatproperties the ratio represents and the context in which these numbers areimportant: Froude Number, Euler Number, Mach Number, Weber Number,Nusselt Number, Prandtl Number.
A liquid of density ? and viscosity ? is pumped at volume flow rate V· through a pump of diameter D. The blades of the pump rotate at angular velocity ? . The pump supplies a pressure rise ΔP to the liquid. Using dimensional analysis, generate a dimensionless relationship for ΔP as a function of the other parameters in the problem. Identify any established nondimensional parameters that appear in your result. Hint: For consistency (and whenever possible), it is wise to choose a length, a density, and a velocity (or angular velocity) as repeating variables.
A simply supported beam of diameter D , length L , and modulusof elasticity E is subjected to a fluid crossflow of velocityV , density ρ , and viscosity μ . Its center deflection δ isassumed to be a function of all these variables. ( a ) Rewritethis proposed function in dimensionless form. ( b ) Suppose itis known that δ is independent of μ , inversely proportionalto E , and dependent only on ρ V 2 , not ρ and V separately.Simplify the dimensionless function accordingly. Hint:Take L , ρ , and V as r e peating variables.
The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.
Let the velocity, u (m/s), specific heat, cp (kJ/(kg K)), and temperature, T (K), be used to define a dimensionless number given by u2cpaTb. The powers must be a=[Blank-1] and b=[Blank-2].
The lift force of an aircraft will be studied in a cryogenic wind tunnel, in which nitrogen at low temperature (183 K) and high pressure (5 atm) is employed as the working fluid. The lift force (F) is known to be a function of the wing span (w), the density of fluid (ρ), the speed of the aircraft (V), the viscosity of fluid (μ), and the speed of sound (c). a. Use dimensional analysis to develop a suitable set of dimensionless terms. data : see picture
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.