By Barenblatt G.I.
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Sample text
In the special case which we have considered this procedure is correct but as a rule, and as we will see further, it is not. 3 Physical similarity 45 Problem 4. Derive the rules for modelling thermal convection in a horizontal fluid layer. We assume that the layer is bounded by smooth rigid isothermal walls: at the upper wall a temperature T0 is maintained and at the lower wall a higher temperature, T0 + δT . Solution. The phenomenon of convection in the gravity field is due to the fact that the density of a fluid usually decreases as it is heated; if this decrease is large enough, the less dense fluid floats from bottom to top.
4 Problems Problem 1. Derive the rules for modelling the steady motion of a body in a fluid that fills a very large vessel. 1 Dimensional analysis and physical similarity 40 The velocity of the body is assumed to be small in comparison with the velocity of sound in the fluid. Therefore the compressibility of the fluid may be neglected, and its density is assumed to be constant. Solution (a) Geometric and kinematic similarity conditions. 10 (b) Dynamic similarity condition. The dimensional governing parameters of the motion are the characteristic length scale of the body, its maximum crosssectional diameter D, for example, the magnitude U of the body’s velocity, the density ρ of the fluid and its viscosity μ.
3 Physical similarity 45 Problem 4. Derive the rules for modelling thermal convection in a horizontal fluid layer. We assume that the layer is bounded by smooth rigid isothermal walls: at the upper wall a temperature T0 is maintained and at the lower wall a higher temperature, T0 + δT . Solution. The phenomenon of convection in the gravity field is due to the fact that the density of a fluid usually decreases as it is heated; if this decrease is large enough, the less dense fluid floats from bottom to top.