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FLUID MECHANICS - CASE STUDY

    Introduction


Problem Description

  Kenneth is planning to enter the doctoral program, and he needs to pass the qualifying exam to be admitted. One question in the recent qualifying exam is from fundamental fluid mechanics. The first part is to derive Bernoulli's equation from Euler's equation. The second part is to use the derived Bernoulli's equation to predict the pressure drop across a nozzle, as shown in the figure. The nozzle is used to accelerate and double the air velocity.
     
    Questions

   

(a) Derive Bernoulli's equation from Euler's equation. (b) What is the pressure difference between the inlet and outlet of the nozzle?

     
    Approach


 
  • Begin the derivation process with Euler's equation in vector form.
  • Use the following vector identity:

             

  • Assume the change in the elevation is negligible when determining the pressure drop, i.e., a horizontal nozzle.
  • The density of air is 1.23 kg/m3.