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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This document was uploaded on 02/07/2014.

Ask a homework question - tutors are online