• By using dimensional analysis, develop a non-dimensional relation between the shear stress and the other parameters governing the flow of incompressible fluid in the fully developed region of a pipe. Make sure you identify the list of relevant parameters and show the rigorous application of the Buckingham theorem and the method of repeating variables. 5) Demonstrate that the yelocitu

• By using dimensional analysis, develop a non-dimensional relation between the shear stress and the other parameters governing the flow of incompressible fluid in the fully developed region of a pipe. Make sure you identify the list of relevant parameters and show the rigorous application of the Buckingham theorem and the method of repeating variables. 5) Demonstrate that the yelocitu

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 5.6P: 5.6 A fluid flows at 5 over a wide, flat plate 15 cm long. For each from the following list,...

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5.6 A fluid flows at 5 over a wide, flat plate 15 cm long. For each from the following list, calculate the Reynolds number at the downstream end of the plate. Indicate whether the flow at that point is laminar, transition, or turbulent. Assume all fluids are at 40°C. (a) air, (b) , (c) water, (d) engine oil.
For the flow of gas between two parallel plates of Fig. 1.7,reanalyze for the case of slip fl ow at both walls. Use thesimple slip condition, δu wall = l ( du/dy ) wall , where l isthe mean free path of the fl uid. Sketch the expected velocityprofile and find an expression for the shear stress ateach wall.
Consider steady viscous flow through a small horizontal tube. For this type of flow, the pressure gradient along the tube, Δp ⁄ ΔL should be a function of the viscosity Y, the mean velocity V, and the diameter D. By dimensional analysis, derive a func- tional relationship relating these variables. Fluid mechanics
A curved blood vessel has an internal diameter ? = 5 mm and a radius of curvature of ?? = 17 mm. Blood has a density of ρ = 1060 kg/m3 and a viscosity of 3.5 cP, and travels at an average velocity of ? = 1 m/s. a) Comment on the nature of the flow with reference to relevant non-dimensional groups. b) Can the flow be modelled using the Hagen-Poisseuile equation? If not, explain what specific assumptions are invalid. c) The viscosity of blood is measured and is shown in Figure Q2. Consider two long straight blood vessels with steady flow. The diameter of the first vessel is 5 mm and the average velocity is 6 cm/s. The internal diameter of the second vessel is 2.2 mm and the average velocity is 50 cm/s. Which vessel would you expect the Hagen-Poisseiulle equation to be more accurate in? Explain your answer (1-2 sentences).
We are given laboratory data, taken by Prof. Robert Kirchhoffand his students at the University of Massachusetts, for thespin rate of a 2-cup anemometer. The anemometer wasmade of ping-pong balls ( d = 1.5 in) split in half, facing inopposite directions, and glued to thin ( 1/4-in) rods pegged toa center axle. There were fourrods, of lengths l = 0.212, 0.322, 0.458, and 0.574 ft. Theexperimental data, for wind tunnel velocity U and rotationrate Ω , are as follows: Assume that the angular velocity Ω of the device is afunction of wind speed U , air density ρ and viscosity μ , rodlength l , and cup diameter d . For all data, assume air is at1 atm and 20 ° C. Defi ne appropriate pi groups for thisthe problem, and plot the data in this dimensionless manner.Comment on the possible uncertainty of the results.As a design application, suppose we are to use thisanemometer geometry for a large-scale ( d = 30 cm) airportwind anemometer. If wind speeds vary up to 25 m/s and wedesire an average…
An important parameter in certain types of fluidflow problems when a free surface is present is the Froudenumber (Fr), which can be expressed in equation form.where p is the density of the fluid, v is a velocity, L is alength, and w is the specific weight of the fluid. Show thatthe Froude number is dimensionless.
Under laminar conditions, the volume flow Q through asmall triangular-section pore of side length b and length Lis a function of viscosity μ , pressure drop per unit length∆p / L , and b . Using the pi theorem, rewrite this relation indimensionless form. How does the volume flow change ifthe pore size b is doubled?
Consider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.
Taylor number (Ta) is used here to describe the ratio between the inertia effect andthe viscous effect. By applying Buckingham Pi’s Theorem, determine an equation forTa as a function of the radius of inner cylinder (r), cylinder tangential velocity (v),fluid dynamic viscosity (μ), gap distance (L) and fluid density (ρ).
By neglecting friction, ( a ) use the Bernoulli equationbetween surfaces 1 and 2 to estimate the volume fl owthrough the orifi ce, whose diameter is 3 cm. ( b ) Why is theresult to part ( a ) absurd? ( c ) Suggest a way to resolve thisparadox and fi nd the true fl ow rate.
i) With Froude’s number as the criterion of dynamic similarity for a certain flow situation, work out the scale factors for velocity, time, discharge, acceleration, and power in terms of the scale factor for length. ii) Compare and contrast the velocity profile of laminar flow and turbulent flow in pipe and comment on them and state any two(2) practical examples.
The head loss for a certain circular pipe is given by hL = 0.0826fL(V.2/D5), where f is the friction factor (dimensionless), L is the pipe length, V. is the volumetric flow rate, and D is the pipe diameter. Determine if the 0.0826 is a dimensional or dimensionless constant. Is this equation dimen sionally homogeneous as it stands?