Consider the flow of a fluid with viscosity  through a circular pipe. the velocity profile in the pipe is given as u(r) = umax(1 - r n /r n ), where umax is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; and u(r) is the flow velocity at any position r. a) (10 points) if n=3, develop an expression for the mass flow rate through the pipe. b) (10 points) what is the average velocity in the pipe?

In an old-fashioned amusement park ride, passengers stand inside a 3.0-m-tall, 5.0-m-diameter hollow steel cylinder with their backs against the wall. the cylinder begins to rotate about a vertical axis. then the floor on which the passengers are standing suddenly drops away! if all goes well, the passengers will “stick” to the wall and not slide. clothing has a static coefficient of friction against steel in the range 0.60 to 1.0 and a kinetic coefficient in the range 0.40 to 0.70. part a what is the minimum rotational frequency, in rpm, for which the ride is safe? express your answer using two significant figures. f f = rpm