2. (Bernoulli's principle) Consider stationary barotropic fluids without viscosity. Here, we consider uniform gravity as an...

 
 

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2. (Bernoulli's principle) Consider stationary barotropic fluids without viscosity. Here, we consider uniform gravity as an external force. (1) Show the Euler's equation of motion becomes v ( 7 ² + P + ²) = * xw ▼ (1) where is the velocity and q = |v1, w Vxw is the vorticity, p is the density, P is the pressure, g is the gravity acceralation, and z is the vertical coordinate (the direction of upward is positive). (2) From Equation (1), show H defined by the following equation is constant along the streamline. q=₁+P+q² = H 2. (Bernoulli's principle) Consider stationary barotropic fluids without viscosity. Here, we consider uniform gravity as an external force. (1) Show the Euler's equation of motion becomes v ( 7 ² + P + ²) = * xw ▼ (1) where is the velocity and q = |v1, w Vxw is the vorticity, p is the density, P is the pressure, g is the gravity acceralation, and z is the vertical coordinate (the direction of upward is positive). (2) From Equation (1), show H defined by the following equation is constant along the streamline. q=₁+P+q² = H

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