Lecture 8

Question 1

dimensional analysis used to create

Answer 1

dimensionless groups

Question 2

any equation can be changed into dimensionless group

Answer 2

power/(force x velocity)

Question 3

basic form of units used in dimensional analysis

Answer 3

Time (T)
Length (L)
Mass (M)
temperature (phi)

Question 4

will not equal 1 if

Answer 4

ratio of something ie reynolds number of efficiency

Question 5

if we have a number variables n and we want to end up with number of dimensionless groups m then we need to make up

Answer 5

n-m equations

Question 6

if we have a number variables n and we have m number of dimensions we need to make up

Answer 6

n-m equations

Question 7

primary variable =

Answer 7

secondary variable^i + secondary variable^j + secondary variable^k

Question 8

first step is to

Answer 8

convert all variables units into basic form ie M L T

Question 9

number of dimension m =

Answer 9

if we have M and L and T = 3 if just two of them = 2 if just 1 = 1

Question 10

number of dimension m =

Answer 10

if we have M and L and T = 3 if just two of them = 2 if just 1 = 1

Question 11

number of variables n =

Answer 11

total number of variables you want to relate

Question 12

number of primary variables =

Answer 12

number of equations you want therefore n - m

Question 13

number of secondary variables =

Answer 13

number of variables - number of primary variables

normally equal to number of dimensions

Question 14

if a variable is already dimensionless then

Answer 14

it gets a group of its own

an angle

Question 15

how to pick primary varaibles

Answer 15

if there are any with identical dimensions pick one
make sure all the primary variables together contain all the dimensions between them
do not select useful common dimensions (velocity and density)
variable you want to determine the function should usually be one of the variables

Question 16

if length and diameter appear

Answer 16

use length as primary as diameter is more common

Question 17

if veloctiy and density appear

Answer 17

do no select normally used as secondary variables

Question 18

second step sub into equation

Answer 18

primary variable = secondary variable^i + secondary variable^j + secondary variable^k
solve to find i j k for all primary variables

Question 19

dimensionless group =

Answer 19

secondary variables to correct powers / primary variable they equal