Problem $4(30$ marks$)$

$($a$)$ The open$-$topped triangular channel shown to the right is

$300m$ long and made of wrought iron. Water

$k\frac{g}{m^3},={10}^{-3}Pa*s)$ flows through the channel at an

average speed of $3\frac{m}{s}.$ The depth remains constant along

the length of the channel and is $h=4cm.$ What is the

friction factor for this flow?

$($b$)$ A soccer ball with $22cm$ diameter travels through $20C$ atmospheric pressure

air at $10\frac{m}{s}.$ Estimate the drag force it experiences.

$($c$)$ Beyblades are spinning top toys that are made to collide with each other in a children's game.

One performance metric of player skill is "rip efficacy." One player's rip

efficacy is measured to be

$362\frac{\text{B}\text{t}\text{u}}{f{t}^2*min}$

What are the dimensions of rip efficacy? Express your answer in terms

of primary dimensions, using the notation followed in class, and

simplified as much as possible.

$($d$)$ A pump, with characteristic curve shown to

the right, pumps $20C$ water at $72\frac{m^3}{h}.$

Estimate the power that the pump delivers to

the fluid in Watts.