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Unformatted text preview: Department of Chemical Engineering and Materials Science University of California, Davis ECH 155A Fluid Properties Goals of the Experiments Determine the specific weight and the viscosity of liquids at room temperature. Also, determine a relationship between the coefficient of drag and the Reynolds number. Compare your findings to established literature values and relationships. Theoretical Background Consider a sphere with diameter d and specific weight γ s , falling at a constant velocity V through a liquid with viscosity μ , specific weight γ l , and density ρ . The forces acting on the sphere are shown in Figure 1 . The expression for the drag force given in Figure 1 is derived from Stoke’s Law and is valid only for small Reynolds number . The drag force on a sphere may also be calculated by: 2 2 D D P V F C A ρ = (1) Where A p is the projected area of the sphere and C D is the coefficient of drag. This general equation for the drag force comes from the definition of the friction factor and Friction force, F k , F D (drag) = 3 πμ Vd F B (buoyancy) F W (weight) Figure 1. Free body diagram of falling sphere. SPHERE which may be arbitrarily expressed as the product of a characteristic area A, a characteristic kinetic energy per unit volume K , and a dimensionless quality f , known as the friction factor K F fAK = (2) In analyzing the phenomena of a settling sphere in an infinite fluid, once the sphere has reached terminal velocity, V ∞ , according to Newton’s Second Law. F = ∑ (3) After some algebraic manipulation, the following expression for μ in terms of γ s, γ l , d , and V can be obtained....
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This note was uploaded on 09/30/2011 for the course ECH 155A taught by Professor Kuhl during the Summer '11 term at UC Davis.
- Summer '11