Static pressure P is measured at two locations along the wall of a laminar boundary layer (Fig. 10-104). The measured pressures are P1and P2distance between the taps is small compared to the characteristic body dimension
b
FIGURE P10-104
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Fluid Mechanics: Fundamentals and Applications
- 1. A fluid is bounded by two parallel plates of infinite width and length as shown in FIGURE Q1. The upper plate moves at 7 m/s, and the lower plate is fixed. The fluid's dynamic viscosity is 1.85X105 N.s/m?. Assume Couette flow with pressure gradient, = 0.1 N/m³. a. Propose the discretization method to solve Couette flow equation with pressure gradient below. Let the number of nodes, n = 9, the distance between the nodes is 0.05 m. Obtain the velocity of all the internal nodes using the matrix inversion method and the iterative method. Compare the results and the effectiveness of both methods (in terms of calculation effort and ease of setting up the problem). + b. Flow shear stress is governed by the following equation ôu Propose the discretization method to solve the above equation and calculate the shear stress at node 1. Describe the condition in tems of the pressure gradient when the shear stress at the bottom plate is zero. Moving plate at Um/s N= N-1 `Fixed plate FIGURE Q1arrow_forwardA fluid flow with mean speed 2 m/s flow over plate of 2.5 m length has kinematic viscosity 2x10 m²/s. 1.328 Use the relation, C = VRe, limit width of plate is drag force (in N) perarrow_forwardMott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forward
- A 5 m of ship model is towed in the water of kinemetic viscosity 1x10^-6 m^2/s at 3.5 m/s. The wetted hull area is 1.4 m^2. What i_s the skin fric_tion drangarrow_forwardConsider a Falling Sphere Viscometer, which is used to measure the viscosity μ of a fluid by observing the terminal velocity of a heavy sphere (density Ps and diameter D) falling under gravity in a column of the fluid (density pf). (a) Use Dimensional Analysis to derive a formula for the drag force exerted on the sphere by the viscous fluid when it is moving at speed v through the fluid. (b) How is the terminal velocity of the sphere related to the fluid viscosity? (c) If the sphere starts from rest, use Dimensional Analysis to predict the timescale over which the sphere will reach its terminal velocity. Please use dimensiona analysis to solve the problem Answr for part a= Fd=KmuVD answer for part b=V=Fd/kmuD Please solve only for part C (part a and b no need to solve)and expalin in detail Thanksarrow_forwardAt a point in a pipe that lay flat ノ water in the pipe flows at a speed of 9.0 mls and has 6-40x 104 Pa a gaoge pressure is Find the gauge pressure at point 2 of pipe that lower than the first point 8.0 m and the cvoss - se ctional| area of the pipe is double of first point . Answer [1.52x105 Pa]arrow_forward
- 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.arrow_forwardFigure 0 shows the change in density of a newtonian fluid with temperature, ing/m^3.Falling spere experiments give average times of 0.2s @ 10 c and 0.23s @ 20 cUsing the equation u=K(ps-pf)tWhere K is found to be 1.34Ps=2300 kg/m3Calculate the viscosity of the fluid at 20 c and 10 carrow_forwardis called a cone-plate viscometer A solid cone of angle 2k, base 1, and density p, is rotat- Ing with initial angular velocity my inside a conical.seat, as shown in Fig. of viscosity u. Neglecting air drag, derive an analytical ex- pression for the cone's angular velocity ) if there is no applied tongue. The device in Fig. The angle of the cone is very small, so thiat sin 0 0, and the gap is filled with the test liquid. The torque M to rotate the cone at a rate 1 is measured. Assuming a lin- ear velocity profile in the fluid film, derive an expression for tiuid viscosity u as a tumction of (M, R. S2, 0). The clearance h is filled with nil Bave C co radius a dwit) dt Fluid I manmot 1Inentia Derive an expression for the capillary height change h for a fluid of surface tension Y and contact angle 0 between two vertical parallel plates a distance W apart, as in Fig. . What will li be for water at 20°C if W = 0.5 mm? A thin plate is separated from two fixed plates by very vis- cous liquids…arrow_forward
- The velocity gradient is 1000 / s. The viscosity is 1.2 X 10 4 N s/m?. The shear stress (N/m) *arrow_forwardConsider 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 mechanicsarrow_forward8:01 32 2.20 Find the dynamic and kinematic viscosities of kerosene, SAE 10W-30 motor oil, and water at a temperature of 38°C (100°F).arrow_forward
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