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 (z_surface as a function of r).

FIGURE P10–44

Transcribed Image Text:

Free surface P = Patm Ug = wr u ₁ = u₂ = 0 Water N W R