Q1, ): A particular laminar boundary layer velocity profile is given by u(y) y 1+ A 2 Um Where y denotes the distance from the center of the channel. a) Determine the expression for the shear stress t(y) as a function of y and other given parameters assuming that d and Um are constant. Find the value of A from table 1 at the end of the questions. b) If A = 0, find the shear stress value at the center of the channel (i.e., at y = 0).
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- For the following questions, Circle the correct answer Q1. We have a steady fully rough turbulent flow of water with constant density in a cylindrical pipe of constant diameter. The height of the uniform roughness elements in the pipe is k.. . . For a fully developed rough turbulent flow in the pipe, the condition ku. -> 70 is the same as k,> 66,. [True/False] V avg The wall shear stress T-pfU/8. It is applicable only for steady fully rough turbulent flow in the pipe. [True/False] The shear stress distribution is linear with the radial distance from the pipe centerline only for laminar flow. [True/False] The head loss per unit length is quadrupled when the discharge is doubled. [True/False] The piezometric pressure drops uniformly along the pipe because the flow is steady along the pipe [True/False]Fluid A oil. abs + Tatm.) : 8. In the figure whown, PluidA is oil (s.9. = 0.80), Fluid B is upecial gage liguid (s.g.:s.g=2A), and x- 1.45 m., determine the clevation z of Fluid A if the prassure at pt. nis 22.06/25 klag and it is three - fourts of the pressure at pt.m. 3. %3D Fluide) sgl. Z :?A Newtonian fluid with absolute viscosity (Greek mu) flows past a flat surface. Due to the no-slip boundary condition, the velocity profile, u(y), develops near the surface and is given by u/U (shown in image provided) where the constant parameters U and delta have dimensions of velocity and length respectively.a) Develop an expression for the shear stress acting in any horizontal plane.b) Determine the shear stress acting on the surface at y = 0 and again at the edge of the boundarylayer, y = delta. (Express your answers in terms of Greek mu, the outer velocity U, and the boundary layer thickness delta.)
- The Stokes-Oseen formula for drag force on a sphere at low speed is given asD = 3dV +916V 2d2, where D is drag, V is velocity, is density, d is the sphere diameter, and is the viscosity coe¢ cient.(a) Using the formula given, Önd the dimensions of the viscosity coe¢ cient. (Donít simply look upthe dimensions; use the formula to show them.) Be sure to show your work. Find the primaryunits of viscosity in SI and British units.(b) Verify that the Stokes-Oseen formula is dimensionally homogeneous.valg, (21535mm 1.15 The pressure difference, Ap, across a partial blockage in an artery (called a stenosis) is approximated by the equation μV Ap - K. 4 + K.(A-1) pv² = K₂ A s.r to zogy nish190 32\V as bonb dignol a 3 basiy noft where V is the blood velocity, u the blood viscosity (FL-2T), p the blood density (ML), D the artery diameter, Ao the area of the unobstructed artery, and A, the area of the stenosis. Determine the dimensions of the constants K, and K. Would this equation be valid in any system of units?The laminar flow of a fluid with a constant viscosity, 4, inside a channel is governed by the following boundary value problem (strong form): d'u dp for y E (0, h) "dy dr u = 0 at y = 0 and y = h vhere u is the fluid velocity and is the pressure drop in the direction of the flow. a) Derive the weak form of the boundary value problem described above.
- Find the kinematic viscosity of an oil having density of 978 Kg/m³. The shear stress at a point in oil is 0.2531 N/m? and velocity gradient at that point is 0.22 per second. * 15.73 stoke 11.76 stoke 13.56 stoke O 20.16 stokeAssignment 3 On Viscosity Calculation - Word TOUT REFERENCES MAILINGS REVIEW VIEW Hyperlink P Bookmark tArt Chart Screenshot Apps for Office Online Video Cross-reference Comment Header Footer Page Number Text Quick WordA Box Parts - ns Apps Media Links Comments Header & Footer (2) Referring to the following figure, the distance between plates is Ay = 0.5 cm, Av: = 10 cm/s, and the fluid is ethanol at 273 K having a viscosity of 1.77cp (0.0177 g/cm s). (a) Calculate the shear stress ty and the velocity (b) gradient of shear rate -/dy using cgs units. (c) Repeat using SI units. A Torce Fdshear berween teoparailel platesfluıd mechanıcs Values for a fluid flowing in a circular pipe are given in the table.a) by writing Newton's law of viscosity,b) Determine the flow behavior of the fluids, show on the graph that they obey the Newtonian or non-Newtonian flow behavior. Calculate the dynamic viscosity values on the graph.c) If the viscosity of the liquid is 0.121 g/cm3, calculate the kinematic viscosity and convert it to the English Unit system.
- Cauchy's ΣF ) equation of motion : pDV/Dt =pg + VT (like pa Newtonian viscous stress relations by the tensor relation : Ti j = - pôij + µ[Əvj/əxi + əvi/axj] where dij is the kroneker delta function (1 for i = T includes pressure and viscous surface forces. into Cauchy's equation, and assume constant viscosity, to get the Navier-Stokes vector eq'ns : pDV/Dt Pg -vp + μ^2 V the acceleration DV/Dt av/at+ (VV)V, which for steady state flow gives DV/Dt =(V.) V. Because (VV) V is a non-linear term on the LHS of the N-S equation Reynolds Number RepVL/μ, a measure of the ratio of inertial to viscous forces. : Patm 10^5 = = N = N = ; pwater 1000; pair 1.2; μwater 10^-3 N s/m^2 ; Hair 2 x 10^-5 N•s/m^2 ; g 9.8 m/s^2 = j; 0 for i j ); NME360L Fluid Mechanics Lab Lab #2: Analysis of Bernoulli's Equation for Fluid Flow through Venturi SERIES This accessory illustrates the circumstances to which Bernoulli's Theorem may be applied. It also explains why in other circumstances the theorem gives an inadequate description of the fluid behaviour. F1-15: Manometer bank (e rereR APPARATU EGL H&L Woter td, > dz dz da dg df 31 Bernoulli's Equation, P/y + V/2g+z=CPLEASE ANSWER CORRECTLY and with full explanation dont do shortcut. you getting 2 $ for it. DONT GIVE WRONG ANSWER I HAVE TO POST IT SECOND TIME. I dont want to give 8 dislikes as given to above expert A two-dimensional flow (x-y plane) is given by u =x +yt and v = - y+xtwhere u and y are the components of the velocity in the x and ydirections respectively, and t is time.A. Is this flow incompressible? Show how you reached yourconclusion.B. Determine the time rate of change of u an v for the fluid particlewhich is located at (x,y) = (2,2) at t = 2 seconds