1- The pressure drop, Ap, along a straight pipe of diameter D has beenexperimentally studied, and it is observed that for laminar flow of agiven fluid and pipe, the pressure drop varies directly with thedistance, {, between pressure taps. Assume that Ap is a function ofD and €, the velocity, V, and the fluid viscosity, u. Use dimensionalanalysis to deduce how the pressure drop varies withpipediameter.A Qulindor with a diametor D doota unrht in g liquidWhon tha

Given, Pressure drop = ∆p Diameter = D Length = l Velocity = V Fluid viscosity = μ

1- The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, l, between pressure taps. Assume that Ap is a function of D and l, the velocity, V, and the fluid viscosity, u. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter.

1- The pressure drop, Ap, along a straight pipe of diameter D has been experimentally studied, and it is observed that for laminar flow of a given fluid and pipe, the pressure drop varies directly with the distance, l, between pressure taps. Assume that Ap is a function of D and l, the velocity, V, and the fluid viscosity, u. Use dimensional analysis to deduce how the pressure drop varies with pipe diameter.

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 5.19P: 5.19 Suppose that the graph below shows measured values of for air in forced convection over a...

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.
5.19 Suppose that the graph below shows measured values of for air in forced convection over a cylinder of diameter D. plotted on a logarithmic graph of as a function of ReD Pr. Write an appropriate dimensionless correlation for the average Nusselt number for these data and state any limitations to your equation.
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 .
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
Consider fully developed flow between two infinite parallel plates separated by distance h, with the top plate moving and the bottom plate stationary. The flow is steady, incompressible, and two-dimensional in the xy-plane. a) Use the first principle (dimensional analysis) to generate a dimensionless relationship for the x-component of fluid velocity u as a function of fluid viscosity μ, top plate speed v, distance h, fluid density ρ, and distance y. b) Name the common dimensionless number formed in (a). Hint: modifying the dimensionless number if necessary.
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.
When small aerosol particles or microorganisms move through air or water, the Reynolds number is very small (Re << 1). Such flows are called creeping flows. The drag on an object in creeping flow is a function only of its speed V, some characteristic length scale L of the object, and fluid viscosity µ. Use dimensional analysis to generate a relationship for the drag force FD as a function of the independent variables.
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 spin rate of a tennis ball determines the aerodynamic forces acting on it. In turn, the spin rate is a§ectedby the aerodynamic torque. If the torque depends on áight speed V , density , viscosity , ball diameter D,angular velocity !, and the fuzz height, hf , Önd the important dimensionless variables for this case. Use V ,, and D as your scaling (repeating) variables.
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
The size d of droplets produced by a liquid spray nozzle isthought to depend on the nozzle diameter D , jet velocity U ,and the properties of the liquid ρ , μ , and Y . Rewrite thisrelation in dimensionless form. Hint: Take D , ρ , and U asrepeating variables.
An important parameter in fluid flow problems involving thin films is the Weber number (We) which can be expressed in equation form as We=[pv^2L/(omega)] where p is the density of the fluid, v is a velocity, L is a length, and (omega) is the surface tension of the fluid. If the Weber number is dimensionless, what are the dimensions of the surface tension (omega)?