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In Section 3.15 we studied the case of the lifting flow over a circular cylinder. In real life, a rotating cylinder in a flow will produce lift; such real flow fields are shown in the photographs in Figures 3.34(b) and (c). Here, the viscous shear stress acting between the flow and the surface of the cylinder drags the flow around in the direction of rotation of the cylinder. For a cylinder of radius R rotating with an angular velocity w in an otherwise stationary fluid, the viscous flow solution for the velocity field obtained from the Navier-Stokes equations (Chapter 15) is
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- 5.71 A cylinder of radius r; rotates at a speed w coaxially inside a fixed cylinder of radius ro. A viscous fluid fills the space between the two cylinders. Determine the velocity profile in the space between the cylinders and the shear stress on the surface of each cylinder. Explain why the shear stresses are not equal.arrow_forward3.2 Perhaps you have felt the end of a garden hose exert a backward force on your hand if (and only if) you have attached a nozzle. Let's estimate this force. Assume that the x-axis is aligned with the end of the hose, and points in the direction of the water flow. (a) Assume that the hose delivers water at the rate of 11 = 1000 cm that the hose has a cross section of 1 cm2. Estimate the speed of the water in the hose. (b) Use your result from part (a) to estimate the impulse [Apæ]enter transferred every second to the nozzle by the water entering the nozzle (one liter of water has a mass of one kg). (c) The nozzle forces the water to leave the nozzle through an opening that has a cross section smaller than that of the hose. Let's assume that the nozzle's cross section is 0.5 cm 2. Estimate the speed at 3 per second to the nozzle, and which the water leaves the nozzle. (d) Estimate the impulse [Apä]leave transferred every second to the nozzle by the water leaving the nozzle. (e)…arrow_forward(B) Fluid is contained in a slot of width h. Find the vėlocity profile if the lower wall oscillates sinusoidally in its own plane while the upper wall is fixed.arrow_forward
- Airplanes usually use their wings to turn: When the plane is tilted at an angle 0, the lift (L) from the wings provides a vertical component and a horizontal component. The direction of the lift is in the plane of symmetry of the plane (up from the wings). Suppose that the plane is tilted at an angle 0 = 29.0° and that it is making an exactly horizontal, circular path at a uniform speed of 455 kph. Take g = 9.80 m.s2 for three significant figures (the value at Sydney). What is the radius of its turn? km. Enter answer herearrow_forward1 A SPHERICAL PORCELAIN BALL, WITH RADIUS R, IS DROPPED WITHOUT INITIAL VELOCITY IN A TEST TUBE CONTAINING GLYCERIN. DURING FALL, THE BALL IS SUBJECT TO THE FOLLO... A spherical porcelain ball, with radius r, is dropped without initial velocity in a test tube containing glycerin. During fall, the ball is subject to the following forces: P its weight; A the thrust of Archimedes; fluid friction force f = k v with k = 6 πrn; n: viscosity (Pa s) of Glycerin, V, velocity Density of Glycerin pg= 1.3 g/mL; density of porcelain pp = 2.3 g/mL; r ball radius= 1.0 cm; n = 1.0 s.Pa; g = 10 N/kg; volume of a sphere V = 4/3 πr³. The speed limit (in m/s) is: 0.11 0.22 0.44 0.33 0.55arrow_forward2.) We are on the space station, so there is no effective gravity. In a small fluid experiment, a small spherical bacteria of 1 mm radius is moving at a speed of +1.50 mm/second horizontally in the fluid. The bacteria has a density of 1500. kg/m^3. (3a) Draw a free-body diagram, labeling all forces and show the likely direction of Fnet (3b) What is the mass of the bacteria? (3c) If the value of the viscosity is 1.25 kg/m/s, then what is the net acceleration experienced by the bacteria at that moment.arrow_forward
- (a) A model low speed centrifugal compressor (a “blower") runs at 430 rpm and delivers 10 m/s of air against a pressure head of 60 mm of water. If the pump efficiency is estimated to be 80%, how much power is required to drive the compressor? (b) A geometrically similar compressor is made with a diameter 1.8 times the size of the model and is required to work against a pressure head of 80 mm of water. Determine the operating speed and the power needed to drive the compressor assuming dynamically similar condi- tions apply.arrow_forwardExample (1-2): A 2.5 cm diameter water jet exerts a force of 90 kN in the direction of flow on a flat plate which is held inclined at an angle of 30° with the axis of stream. Find the rate of flow.arrow_forwardProblem 6.2 The gap between a moving plate of height H and a stationary wall is filled with an incompressible liquid with density pliq. The plate is pushed to the right at a constant speed Vplate. At the bottom sliding joint, there is a seal to prevent leakage. The gap width x and the liquid height y are continuously changing with time. The length dimension L into the page is constant. Side View: H V plate seal X Stationary wall (a) Determine rate of change of the liquid width with time, (d x/d t) in terms of the given variables (i.e., Vplate). (b) Assume the moving plate height H is tall enough that the liquid does not spill over. Determine the rising rate of the liquid top surface (d y/d t) in terms of the given variables. (c) Assume the moving plate height H is too short and the liquid spills over as the plate keeps moving. Determine the mass flow rate of the spillage in terms of the given variables.arrow_forward
- Example (1-1): Find the force exerted by a 5 cm diameter water jet directed against a flat plate held normal to the exit of stream. The velocity of the jet is 35 m/s. Example (1-2): A 2.5 cm diameter water jet exerts a force of 90 kN in the direction of flow on a flat plate which is held inclined at an angle of 30° with the axis of stream. Find the rate of flow.arrow_forwardO2. Two immiscible liquids of equal thickness h are being sheared between a fixed and a moving plate, as in Fig. 2. Gravity is neglected, and there is no variation with x. Find an expression for (i) the velocity at the interface and (ii) the shear stress in each fluid. Assume steady laminar flow. Fluid layer Fixed Fig. 1 Fig. 2arrow_forwardQ1) A new computer drive is proposed to have a disc, as shown in Fig. 1. The dise is to rotate at 9,000 rpm, and the reader head is to be positioned 0.011 in. above the surface of the disc. Estimate the shearing force on the reader head as a result of the air between the disc and the head. Use v air = 1.47 x 10-5 m2/s. Stationary reader head 6 mm dia. 9,000 rpm 0.011 mm 55 mm Rotating disc Fig. (1).arrow_forward
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