Introduction to Fluid MechanicsPrentice-Hall, 1968 - 457 pages |
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Page 84
... Divergence Theorem The divergence theorem , + [ v.Gdv - SG.nd 7.GdV G⚫ndA = ( 3.3-1 ) is a necessary mathematical tool for developing the differential equations of mass , momentum , and energy . In addition , it is very useful in ...
... Divergence Theorem The divergence theorem , + [ v.Gdv - SG.nd 7.GdV G⚫ndA = ( 3.3-1 ) is a necessary mathematical tool for developing the differential equations of mass , momentum , and energy . In addition , it is very useful in ...
Page 87
... divergence theorem for a scalar is obtained . VS dv = S Sn dA ( 3.3.17 ) The value of this result may be demonstrated by applying it to the linear momentum equation for a static fluid , which , in Chap . 2 , was 0 ... Divergence Theorem 87.
... divergence theorem for a scalar is obtained . VS dv = S Sn dA ( 3.3.17 ) The value of this result may be demonstrated by applying it to the linear momentum equation for a static fluid , which , in Chap . 2 , was 0 ... Divergence Theorem 87.
Page 217
... divergence theorem † to the two area integrals in Eq . 7.2-2 allows us to put all the terms under the same integral sign , and we readily obtain the stress equations of motion . a ( pv ) + ▽ • ( pvv ) = pg + ▽ • T at ( 7.2-3 ) ...
... divergence theorem † to the two area integrals in Eq . 7.2-2 allows us to put all the terms under the same integral sign , and we readily obtain the stress equations of motion . a ( pv ) + ▽ • ( pvv ) = pg + ▽ • T at ( 7.2-3 ) ...
Contents
Introduction | 1 |
Fluid Statics and OneDimensional Laminar Flow | 32 |
Kinematics | 75 |
Copyright | |
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Aa(t analysis apply area integral Bernoulli's equation boundary condition boundary layer channel Chap choke flow constant continuity equation control volume coordinates curve cylinder density derivative determine differential equations dimensionless divergence theorem drag coefficient energy equation equations of motion experimental expression flat plate friction factor function given by Eq hydraulic jump illustrated in Fig incompressible flow index notation indicates isentropic Mach number macroscopic balances mass balance material volume mechanical energy balance momentum balance nozzle obtain pipe pressure problem rate of change rate of strain region result Reynolds number Reynolds transport theorem scalar components shear stress shown in Fig side of Eq solution streamline stress tensor stress vector supercritical flow surface forces temperature time-averaged tube turbulent flow unit v₂ Va(t velocity profile viscous viscous dissipation viscous effects volumetric flow rate wave yields zero дл др ду дх