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Fluid Kinematics

  Fluid Kinematics Fluid Kinematics  deals with the motion of fluids such as displacement, velocity, acceleration, and other aspects. This topic is useful in terms of the exam and the knowledge of the candidate. Kinematics is the branch of classical mechanics that describes the motion of bodies and systems without consideration of the forces the cause the motion. Types of Fluid Flows Fluid flow may be classified under the following headings; Steady & Unsteady Flow Uniform & Non-uniform Flow Steady uniform flow Conditions do not change with position in the stream or with time. E.g. flow of water in a pipe of constant diameter at a constant velocity. Steady non-uniform flow Conditions change from point to point in the stream but do not change with time. E.g. Flow in a tapering pipe with the constant velocity at the inlet. Unsteady uniform flow At a given instant in time the conditions at every point are the same but will change with time. E.g. A pipe of constant diameter connecte
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Expression for capillary rise and capillary fall - Jurin's law

  Expression for capillary rise and capillary fall - Jurin's law Expression for height in Capillary rise Consider a narrow glass tube of diameter of d dipped in a liquid (say water). Water in the tube will rise above the adjacent liquid level. It is called capillary rise. Let σ = Surface tension of liquid. ϴ = Angle of contact between the glass tube and the liquid surface. h = Height of liquid column in glass tube. Under equilibrium, two forces are acting on the water inside. The first one is weight of water column and second is the upward force acting on water due to surface tension. The weight of liquid of height h should be balanced by the force at liquid surface. This force at surface of liquid is due to surface tension. The weight of liquid of height h in the tube = Volume x ρ x g = (π/4)d 2  x h x ρ x g Here ρ = density of liquid g = acceleration due to gravity. The vertical component of surface tensile force = surface tension x circumference x cosϴ = σ x πd x cosϴ At equilib

capillary rise

A liquid of density  ρ ρ  and surface tension  σ σ  rises in a capillary of inner radius  r r  to a height h = 2 σ cos θ ρ g r h = 2 σ cos ⁡ θ ρ g r where  θ θ  is the contact angle made by the liquid meniscus with the capillary’s surface. The liquid rises due to the forces of adhesion, cohesion, and surface tension. If adhesive force (liquid-capillary) is more than the cohesive force (liquid-liquid) then liquid rises as in case of water rise in a glass capillary. In this case, the contact angle is less than 90 deg and the meniscus is concave. If adhesive force is less than the cohesive force then liquid depresses as in case of mercury in a glass capillary. In this case, the contact angle is greater than 90 deg and the meniscus is convex. The formula for capillary rise can be derived by balancing forces on the liquid column. The weight of the liquid ( π r 2 h ρ g π r 2 h ρ g ) is balanced by the upward force due to surface tension ( 2 π r σ cos θ 2 π r σ cos ⁡ θ ). This formula can als