Derivations - Fluid Mechanics Questions

  1. Derive a general equation for the variation of pressure due to gravity from point to point in a static fluid.
  2. Derive an expression for the pressure difference across two limbs of a differential manometer containing two gauge fluids, mutually immissible. What factors influence the sensitivity?
  3. Derive the equation of continuity for an incompressible flow. State the importance of the equation.
  4. By applying momentum balance to the steady flow of a fluid inside a pipeline, obtain the Bernoulli's equation. Indicate the corrections necessary to the equation for application to real situations.
  5. Derive Euler's equation of motion along a streamline in differential form and obtain Bernoulli's equation in the integral form for the flow of an incompressible fluid.
  6. Derive the Hagen-Poiseuille equation for laminar flow through a circular pipe. State the limitations of the equation.
  7. Show that the average velocity of the fluid flowing through a circular pipe under laminar conditions is half that of the maximum velocity.
  8. Consider the flow of a Newtonian fluid in a pipe having roughness 'k'. By dimensional analysis, develop an equation relating the frictional pressure drop in terms of the following:
  9. r - density of fluid
    m
    - viscosity of fluid
    v - velocity of fluid
    D - diameter of pipe
    L - length of pipe
    k - roughness