Using the results of Prob. 1044, calculate the Bernoulli constant as a function of radial coordinate r.

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Using the results of Prob. 10–44, calculate the Bernoulli constant as a function of radial coordinate r.


Data from problem 44

Water at T = 20°C rotates as a rigid body about the z-axis in a spinning cylindrical container (Fig. P10–44). There are no viscous stresses since the water moves as a solid body; thus the Euler equation is appropriate. (We neglect viscous stresses caused by air acting on the water surface.) Integrate the Euler equation to generate an expression for pressure as a function of r and z everywhere in the water. Write an equation for the shape of the free surface (zsurface as a function of r).


FIGURE P10–44

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