In all problems draw a schematic, state assumptions, show the process to simplify your equations, and

box your final answer for full credit.

Chapter $11$

$11\mathrm{.}1($Welty $11\mathrm{.}1,9$ pts$)$ The power output of a hydraulic turbine depends on the diameter $D$ of the

turbine, the density $p$ of water, the height $H$ of water surface above the turbine, the gravitational

acceleration $g,$ the angular velocity $$ of the turbine wheel, the discharge $Q$ of water through the turbine,

and the efficiency $$ of the turbine. By dimensional analysis, generate a set of appropriate dimensionless

groups.

$11\mathrm{.}2($Welty $11\mathrm{.}2,6pts)$ Through a series of tests on pipe flow, H$.$ Darcy derived an equation for the

friction loss in pipe flow as

$h_L=f(\frac{L}{D})\frac{v^2}{2g}$

in which $f$ is a dimensionless coefficient that depends on $($a$)$ the average velocity of the pipe flow; $($b$)$ the

pipe diameter $D$; $($c$)$ the fluid density $$; $($d$)$ the fluid viscosity $$; and $($e$)$ the average pipe wall uneveness

$e($length$).$ Using the Buckingham $$ theorem, find a dimensionless function for the coefficient $f.$

$11\mathrm{.}3($Welty $11\mathrm{.}3,6pts)$ The pressure rise across a pump $P($this term is proportional to the head

developed by the pump$)$ may be considered to be affected by the fluid density $,$ the angular velocity $,$

the impeller diameter $D,$ the volumetric rate of flow $Q,$ and the fluid viscosity $.$ Find the pertinent

dimensionless groups, choosing them so that $P,Q,$ and $$ each appear in one group only.

$11\mathrm{.}4($Welty $11\mathrm{.}4,9pts)$ The rate at which metallic ions are electroplated from a dilute electrolytic

solution onto a rotating disk electrode is usually governed by the mass diffusion rate of ions to the disk.

This process is believed to be controlled by the following variables:

Obtain the set of dimensionless groups for these

variables where $k,{}_2$ and $D$ are kept in separate groups.

How would you accumulate and present the

experimental data for this system?

$11\mathrm{.}5($Welty $12\mathrm{.}17,6$ pts$)$ A baseball has a

circumference of $9^{\frac{1}{4}}$ in$.$ and a weight of $5^{\frac{1}{4}}$ ounces. At

$95$ mph determine

a$.$ the Reynolds number

b$.$ the drag force

c$.$ the type of flow $($see the illustration$)$