Question

A cyclindrical container filled with a liquid of density p rotates about an axis through its center with an angular velocity w. A Cartesian coordinate system in standard orientation is introduced with its origin at the lowest point on the fluid surface. The pressure above the liquid surface is P_0.

(a) Notice that a thin imaginary tube with cross-section area A lies along the -axis. Draw a free boy diagram for a slice of liquid within this tube, lying between generic coordinates x and x+dx. Seperately list the x-components of all relevant force vectors and the accel vector

(b) Substitute your results from (a) into Newton's second law. Derive a differential equation for pressure along the x-axis

(c) Integrate your result from (b) to obtain P(x) along the x-axis

(d) Derive a function y(x) which gives the shape of the liquid surface

(e) A cork (density pc < p) is attatche to the bottom of the container by a light string, at some nonzero distance from the center. Does the string bend in towars the center of the container or outward towards the walls? Explain.

Answer 1

A k 2. L. becaur aƠ we move away