fluidmech

D if the water velocity is reduced to 05 ms show that

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Unformatted text preview: Ns/m2. Show that the flow is laminar and hence deduce the pressure loss per metre length. (150 Pa per metre). 2. Oil flows in a pipe 100 mm bore diameter with a Reynolds’ Number of 500. The density is 800 kg/m3. Calculate the velocity of a streamline at a radius of 40 mm. The viscosity µ = 0.08 Ns/m2. (0.36 m/s) 3. A liquid of dynamic viscosity 5 x 10-3 Ns/m2 flows through a capillary of diameter 3.0 mm under a pressure gradient of 1800 N/m3. Evaluate the volumetric flow rate, the mean velocity, the centre line velocity and the radial position at which the velocity is equal to the mean velocity. (uav = 0.101 m/s, umax = 0.202 m/s r = 1.06 mm) 4. Similar to Q6 1998 a. Explain the term Stokes flow and terminal velocity. b. Show that a spherical particle with Stokes flow has a terminal velocity given by u = d2g(ρs - ρf)/18µ Go on to show that CD=24/Re c. For spherical particles, a useful empirical formula relating the drag coefficient and the Reynold’s number is 24 6 CD = + + 0.4 Re 1 + Re Given ρf = 1000 kg/m3, µ= 1 cP and ρs= 2630 kg/m3 determine the maximum size of spherical particles that will be lifted upwards by a vertical stream of water moving at 1 m/s. d. If the water velocity is reduced to 0.5 m/s, show that particles with a diameter of less than 5.95 mm will fall downwards. © D.J.DUNN 21 5. Similar to Q5 1998 A simple fluid coupling consists of two parallel round discs of radius R separated by a a gap h. One disc is connected to the input shaft and rotates at ω1 rad/s. The other disc is connected to the output shaft and rotates at ω2 rad/s. The discs are separated by oil of dynamic viscosity µ and it may be assumed that the velocity gradient is linear at all radii. Show that the Torque at the input shaft is given by T = πD 4 µ (ω1 − ω 2 ) 32h The input shaft rotates at 900 rev/min and transmits 500W of power. Calculate the output speed, torque and power. (747 rev/min, 5.3 Nm and 414 W) Show by application of max/min theory that the output speed is half the input speed when maximum output power is obtained. 6. Show that for fully developed laminar flow of a fluid of viscosity µ between horizontal parallel plates a distance h apart, the mean velocity um is related to the pressure gradient dp/dx by um = - (h2/12µ)(dp/dx) Fig.2.11 shows a flanged pipe joint of internal diameter di containing viscous fluid of viscosity µ at gauge pressure p. The flange has an outer diameter do and is imperfectly tightened so that there is a narrow gap of thickness h. Obtain an expression for the leakage rate of the fluid through the flange. Fig.2.13 Note that this is a radial flow problem and B in the notes becomes 2πr and dp/dx becomes -dp/dr. An integration between inner and outer radii will be required to give flow rate Q in terms of pressure drop p. The answer is Q = (2πh3p/12µ)/{ln(do/di)} © D.J.DUNN 22 3. TURBULENT FLOW 3.1 FRICTION COEFFICIENT The friction coefficient is a convenient idea that can be used to calculate the pressure drop in a pipe. It is defined as follows. Cf = 3.1.1 Wall Shear Stress Dynamic Pressure DYNAMIC P...
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This document was uploaded on 02/07/2014.

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