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
- Take the full-blown Couette flow as shown in the figure. While the upper plate is moving and the Lower Plate is constant, flow occurs between two infinitely parallel plates separated by the H distance. The flow is constant, uncompressed, and two-dimensional in the X-Y plane. In fluid viscosity µ, top plate velocity V, distance h, fluid density ρ, and distance y, create a dimensionless relationship for component X of fluid velocity using the method of repeating variables. Show all steps in order.arrow_forward5arrow_forwardBooks on porous media and atomization claim that the viscosityμ and surface tension Y of a fl uid can be combinedwith a characteristic velocity U to form an important dimensionlessparameter. ( a ) Verify that this is so. ( b ) Evaluatethis parameter for water at 20°C and a velocity of3.5 cm/s. Note: You get extra credit if you know the nameof this parameter.arrow_forward
- 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_forwardI need the answer as soon as possiblearrow_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_forwardI need correct solution Previous solution in chegg and bartleby are incorrect So don't copypaste in chegg and bartleby Provide correct solution Answer is 0.02marrow_forward
- The torque M required to turn the cone-plate viscometer inFig. depends on the radius R , rotation rate Ω , fl uidviscosity μ , and cone angle θ . Rewrite this relation indimensionless form. How does the relation simplify it if itis known that M is proportional to θ ?arrow_forwardfluid mechanics experts please solve with details and give reasons for steps if needed. parts a b and c are solved . in this question i want the last two questions. please use the P that isobtained from g part in h part with P0 as example. σxx= -P + τxx = 0.125 ρ - P0 + 2μ = 0.75 Paarrow_forwardEarrow_forward
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