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- An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is rt of this book may be reproQA An incompressible fluid (kinematic viscosity, 7.4 x10-7 m2/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is (a) 0.651 x 10-3 (c) 6.51 (b) 0.651 (d) 0.651 x 1031. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?
- An incompressible fluid (kinematic viscosity, 7.4 x10-7 m²/s, specific gravity, 0.88) is held between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm between these plates; the shear stress in Pascals on the surface of top plate is (a) 0.651 x 10-3 (c) 6.51 (b) 0.651 (d) 0.651 x 103(b) A Formula 1 team tests their car in a wind tunnel at a scale of 50%, at a speed of Vwinarunnet = 50 m/s. The measured downforce at this speed is Foownforce.WT = 3000 N and the model reference area is Aref wT = 0.5 m?. 1. Find the downforce magnitude on the full-scale race car at the same Reynolds number. Assume constant air density p = 1.2 kg/m. II. It is said that F1 cars could travel upside down, as shown below. At what speed should the full-scale car travel to achieve this, if its mass is m = 740 kg? The acceleration of gravity is g = 9.81 m/s?. Downforce WeightA viscous fluid of density 1200 kg/m3 and viscosity 0.9 Pa.s is confined in a spacing of 0,01 m between two parallel and horizontal plates of length 0,6 m and width 0,6 m. The upper plate is pulled with a uniform and steady speed of 0,7 m/s in its own plane. The lower plate is stationary. Viscous fluid flow is laminar steady and incompressible. a) What is the magnitude of mass flow rate in spacing (in kg/s)? b) What is the magnitude of maximum shearing stress in the flow field (in Pa)? c) What is the frictional force over the lower plate surface (in N )? d) What is the frictional power lost in pulling the upper plate (in W)?
- A plate 0.05mm distance from a fixed plate moves at 1.25 m/s and required a force per unit area of 3 Pa to maintain this speed by using an oil of specific gravity 0.65. Find the dynamic viscosity in centipoise and kinematic viscosity in stokes of the fluid between the plates. Calculate the specific weight in kN/m³, density, and the specific gravity of a liquid having a volume of 662900 cm and weight of 55 kNA seA A, soA A solid cylinder of diameter d, length and density p, falls due to gravity inside a pipe of diameter D. The clearance between the solid cylinder and the pipe is filled with a Newtonian fluid of density p and u. For this clearance fluid, the terminal velocity of the cylinder is determined to be V, assuming a linear velocity profile. However, if the clearance fluid was changed to a Newtonian fluid of density 2p and viscosity 2u, then for an assumed linear velocity profile, the terminal velocity of the cylinder was determined to be V,. From the results of these experiments, one may write that (A) V = V (C) 2 V= V (B) V=2 V, (D) V= 4 V1- Reynolds number is a dimensionless number represent .....to .. 2- The velocity profile of the flow between two parallel plates is linear if the pressure gradient equal and parabolic if the pressure gradient has a .... 3- In the sink and source flow the potential function is represented as.. ...... and the stream function is represented as **** 4- In the laminar boundary layer, the .............. is the dominant reason for the loss while in turbulent boundary layer the is dominant. 5- For inviscid flow, there are no shear stresses the only forces acting on a fluid element are ....... and. *****
- A 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) perPipelines are cleaned by pushing through them a closefitting cylinder called a pig . The name comes from thesquealing noise it makes sliding along. Reference 50describes a new nontoxic pig, driven by compressed air, forcleaning cosmetic and beverage pipes. Suppose the pigdiameter is 5-15/16 in and its length 26 in. It cleans a6-in-diameter pipe at a speed of 1.2 m/s. If the clearance isfi lled with glycerin at 20 8 C, what pressure difference, inpascals, is needed to drive the pig? Assume a linear velocityprofi le in the oil and neglect air drag.U L CD Fig.1. Airflow on a cylinder U U U/2 L/2 L/2 1. When a uniform stream flows past an immersed thick cylinder, a broad low-velocity wake is created downstream, idealized as a V shape in Fig. 1. Pressures p1 and p2 are approximately equal. (a) If the flow is two-dimensional and incompressible, with width b into the paper, derive a formula for the drag force F on the cylinder. (b) Rewrite your result in the form of a dimensionless drag coefficient based on body length F pU²bL