# Approximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.

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1 Appendix

2 FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface tension with air (Njm) Acetone x X 10- Benzene x X 10- Carbon tetrachloride I x X 10- Glycerin x 10- n-octane x 10- n-pentane x 10- Mercury x X 10-1 Sea-water I x X 10- Water x X 10- Gases Density (kg/m'') Dynamic viscosity (N s/m ) Air Carbon dioxide Carbon monoxide Hydrogen Methane Nitrogen Oxygen Propane X X X X X X X X

3 APPENDIX Properties of geometric shapes Circle Diameter d 0_ _ 0 Area: 7rd /4 About 0-0, Ie = 7rd 4j64 Rectangle b Area: bh About 0-0, Ie = bh j1 Triangle 1 h O '--...:::;:>;E---\--0 Area: bhj Ii =h/ About 0-0, Ie = bh /6 About X-X, Ix = bh j1 xl~----""-----~ --X l b J Parallel axis theorem Or-f-- o --x Second moment of area about axis 0-0 through the centroid C is t., Second moment about the parallel axis X - X is Ix. Distance between axes is d. Then lx = Ie + Ad 401

4 FLUID MECHANICS Answers to test exercises and further problems Programme 1 Test exercises Further problems kn/m MN/m 65 N/m 0.0 N s/m 5.19 kn/m 1.0 kn per m; 1.9 kn 4.7 N/m g; 4.95 mm kg/m! mm (negligibly small) 6 8.6mm Programme kn m 8.4 kn 199 kn (a).6 kn 559 N at to horizontal (b) m 4 09 kn (c) 1.4 kn N at 1 mm from C 4.1 kn to left 5.0 kn upwards Programme m m 1.07 m m 0.49 m; stable b/fi 4 Reduced by 0.57 m; m now unstable m 5 (a) 0. m (b) 104 mm lower relative to ship (c) m (d) 5 s Programme m/s; 1.65 m; I.5 m/s 0.75 m 0.10 m lower 59 N/m 894 m/s (a) 9.6 m/s kn/m (b) 456 kn/m 40

5 APPENDIX Programme mjs (a). mjs; (b) 0.17 kgjs (a) 18.7 kn jm (b) 18 W mjs 0.70 mjs 8691/min 44 kn/m ; 691 I/min Programme N, at 1 to the vertical.0 kn, at 0 to the horizontal 10 N to the right N, at 9 above horizontal 56 m/s A(p + pu ) 6.4 kn to the right (a) 7 mjs (b) 8.1 N downwards; 140 N to the right Programme 7 (i) k~j; (ii) [~] (i) consistent (ii) not consistent (first and second terms [ML jt ] ; third term [MLjT ]) Programme 8 1 (6.pfJpQ); or some power of this ratio, or its reciprocal (a) (FjputP) and (P/pu ), for example. Other forms, such as the product of these, are possible, and are equally correct. Programme 9 (a) 66.1 x 10 ; turbulent (b) approx. (c) 57 knjm 100 kn/m 861jmin I Njm 7. knjm per metre length 1.1 (a) 0.61 m (b) 1.4 m (c) 54 I/min 7.8 Ijs; 109 kw; 177 m; 17 mm diameter 40

6 INDEX aerofoil 15, 45 lift force on 45 aircraft, vertical take-off force on 79 air lock 195 angle of contact 48 angle of incidence 45 Archimedes' principle 9, 110 argument, dimensions of 99 barometer 6 Bernoulli's equation 174 derivation for a pipe with losses 8 and venturi meter 11 bluff body 4 bucket, Pelton wheel 57,61,64 Buckingham's theorem 1 buoyancy 9,110 centre of definition 11 carburettor 18 car ferries, stability of 14 centre of buoyancy definition 11 centre of pressure 66, of circular gate 80 definition 66 of rectangular gate 81 of T-shaped plate 88 centroid of a plane area chord of aerofoil 45 closed-circuit wind tunnel 6 coefficient of contraction coefficient of discharge for orifice for venturi meter 17 coefficient of drag 4 coefficient of lift 4 coefficient of velocity compressibility consistent set of units 91 continuity principle 156 and mean velocity 158 contraction coefficient of in a pipe 159 control surface 16, 5 conversion of units 84 dependent dimensionless ratios dependent variables 1 derivative, dimensions of 0-5 derived unit 91 development of flow pattern in a pipe 6, 65, 66 diffuser 160,11,4 angle 4 efficiency 4 dimensional formula 95 dimensionless quantities 98 dimensionless ratios dependent independent presentation of data in terms of dimensions discharge, coefficient of 157 for orifice for venturi meter 17 displacement 141 drag coefficient 4 drag force on sphere 0 dynamic pressure dynamic similarity 5, 41 dynamic viscosity 6 ears, popping 19 efficiency, diffuser 4 elevation 189, 86 energy 168 loss in orifice meter loss in venturi meter 5 entrance to a pipe, development of flow pattern in 6, 65, 66 equations, consistency of 8 experimental results, presentation in terms of dimensionless ratios fabric, cutting with water jet 00 fittings, head loss in 90 flaps

7 INDEX flow laminar 5 turbulent 5 flow rate over sharp-edged weir 9 over v-notch weir 1 frame of reference, moving 196 free jet 5 friction factor 69 European version 69 in laminar flow 71 USA version 69 friction loss in non-circular pipes 9 in a pipe 74 fully developed flow in a pipe 64, 65, 66 gauge I gauge pressure 18 negative geometric similarity 41 grade line, hydraulic 19 Hagen 60 Hagen-Poiseuille equation 59, 64 head 18, 189 pressure 18, 86 total 189 velocity 189, 86 head loss in a pipe 74, 85 hydraulic grade line 19,87, 91 hydraulic mean depth 9 hydrometer 4 hydrostatic force 65 on a circular window in a tank 7 on a curved surface on a dished end 9 on the end of a tank 66, 68 on a hemispherical tank end 96 on an inclined plane area, expression for 71 on a pipe elbow 94 on a plane area on a quadrant tank end 98 on a radial sluice gate 10 on rectangular sluice gate 7, 74 incidence, angle of 45 inclined manometer 4 incompressibility independent dimensionless ratios independent variables 1 injector 180 inverted V-tube 1 jet free 5 submerged 5 jet engine thrust 48 jet of water, force of 46, 6 on moving Pelton bucket 64 on moving plate 6 kinematic viscosity 79 laminar flow 5 friction factor in 71 pressure drop in a pipe 57 velocity profile in a circular pipe 59 leather, cutting with water jet 00 lift 45 coefficient of 45 liquid cargo, effect on stability 19 locomotive picking up water 197 manometer -5 two-fluid 7 inclined 4 mass flow rate 157 mean velocity and continuity principle 158 meniscus 49 for mercury in glass 50 metacentre 14 metacentric height 1-8 definition 16 experimental determination 17-0 metacentric radius 1 calculation from geometry 18 model testing 4 momentum 44 rate ofchange of Moody chart 7 moving frame of reference 196 newton 91 Newtonian fluid 5 Newton's laws ofmotion 4,4,45,46 non-eircular pipes, friction loss in 9 numerical data, presentation in terms of dimensionless ratios

8 INDEX orifice coefficient of contraction coefficient of discharge coefficient of velocity flow through 1 orifice meter 8 advantages and disadvantages energy loss in in inclined pipe 1 parallel axis theorem 85 Pelton wheel 56 period of rolling of ship 144 piezometer, 188, 0 pipe bend force on force on pipe elbow, force on 71 pipe fittings, head loss in 90 pitching motion 19 pitot-static tube 09 pitot tube 0, 04 plan area (of aerofoil) 45 Poiseuille 60 Poiseuille equation 59, 64 power series, dimensions of terms 99 pressure 14-1 definition 14 gauge 18 dynamic 0 stagnation 0 static 187, 09 total 0 pressure drop across orifice across venturi 5 pressure head 189, 86 pressure loss in a pipe 74 measurement variation in a venturi 178 variation with depth 16 relative density 4 Reynolds number 4, 5, 4, 5, 67, 69 Reynolds, Osborne 4, 5 ripples, speed of motion 8 road sign, wind force on 9 road vehicle, drag force on 4 rocket, force on a stationary 4, 44 rolling motion 19 roll-on, roll-off ferries, stability of 14 roughness, internal, of pipes 71 sea waves, speed of 5 second moment of area 79 sensitivity 9 shear stress at wall of a pipe 55 similarity 5, 41 dynamic 5, 41 geometric 41 siphon 19 specific gravity 4 stability of a floating object 1-8 effect of liquid cargo on 19 of a submerged body condition for 118 stagnation point 0 stagnation pressure 0 static pressure 187, 09 static tapping 188 streamline 15 streamtube 154 submerged jet 5 surface tension 45-50, 8 definition 45 tapered pipe, force on 7 testing models 4 throat (of venturi etc.) 11 total head line 87, 91 total pressure 0 turbine, Pelton 56 turbulent flow 5 in a pipe, velocity profile 66 units consistency of 8 consistent set of 91 conversion of 84 V-tube inverted 1 vane, force on 49, 54 vapour lock 195 variables dependent 1 independent 1 velocity coefficient of 407

9 INDEX gradient 10, 59 head 189, 86 of liquid falling from a pipe 177 vena contracta 1 venturi meter 11 advantages and disadvantages coefficient of discharge 17 inclined 14 venturi, pressure variation in 178 vertical take-off aircraft, forces on 79 viscometer 59 viscosity 4-1, 0, 57 coefficient of 5, 11 dynamic 79 kinematic 79 v-notch weir, flow rate over 1 volume flow rate 157 water jet cutting 00 waves, speed of on the surface of the sea 5 weir, sharp-edged 9 windmill, power 0 wind tunnel, closed-circuit 6 work

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