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MT-264 Fluid Mechanics

MT-264 Fluid Mechanics. Lecture # 09 Syed Ehtisham Gillani. Fluid Kinematics. What is Reynold’s Number? It is defined as “ the ratio of inertia forces to viscous forces”

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MT-264 Fluid Mechanics

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  1. MT-264 Fluid Mechanics Lecture #09 Syed Ehtisham Gillani

  2. Fluid Kinematics

  3. What is Reynold’s Number? • It is defined as “ the ratio of inertia forces to viscous forces” • It’s a dimensionless number which is used in fluid mechanics to predict the flow pattern of fluid in different flow situations.

  4. Rotational & Irrotational Flow • The flow in which the fluid particle while flowing along stream lines, also rotate about their own axis is called as rotational flow. • Example: Motion of a liquid in a rotating cylinder. (also known as forced vortex) • The flow in which fluid particles while flowing along streamlines, do not rotate about their axis is called irrotational flow. • Example: Draining of the bath tub (Free vortex).

  5. Continuity Equation • Continuity equation shows that mass flow rate of a fluid remains the same at every position of a pipe/tube that has a single entry and exit for fluid flow. • Continuity equation is based upon Law of conservation of mass.Which means that the mass of fluid entering a pipe/tube remains the same as it exits regardless of the shape/area of the pipe/tube. • Continuity equation is applicable to ideal fluids (Incompressible, steady and nonviscous)

  6. Continuity Equation • m1 = m2 A1V1 = A2V2 Q1 = Q2

  7. Continuity Equation

  8. Continuity Equation • The Area (A) and Velocity (V) are inversely proportional to each other. • Which means that for the same value of Discharge (Q), decreasing the area will result an increase in velocity and vice versa.

  9. Continuity Equation Mean Velocity Velocity of fluid in pipe is not uniform across the section area. Therefore a mean velocity is used and it is calculated by the continuity equation for the steady flow as: V = Q/A

  10. Continuity Equation Sample Problem

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