How many grams is one molecule of calcium oxide?
1 answer:
You might be interested in
We know that
So, the volume of the entire building is
The flow capacity of the fan
As
For the other part we know
The diameter is,
<em>**Note 60 is for the minutes</em>
<em />
Answer:
Explanation:
Given that,
Omega is a function of the following
ω = f(b, h, v, ρ, k)
Where, all unit have a dimension of
ω = T^-1
b = L
h = L
V = LT^-1
ρ = FL^-4T²
k = FL
Then,
From the pie theorem
The required pi term is 6—3 = 3 terms,
So, we use V, p and b as a repeating term.
For first pi
π1 = ω•b^a•v^b•ρ^c.
Since
ω= T^-1, b = L, v = LT^-1 and
ρ= FL^-4T²
Since π is dimensionless then,
π = F^0•L^0•T^0
(T^-1)•(L^a)•(LT^-1)^b•(FL^-4T²)^c = F^0•L^0•T^0
Rearranging
F^0•L^0•T^0 = F^c•T^(2c-b-1)• L^(a+b-4c)
Comparing coefficient
c = 0
2c - b - 1 = 0
b = 2c - 1 = 0 - 1 = -1
a + b - 4c = 0
a = 4c - b = 0 - -1 = 0+1
a = 1
Then, a = 1, b = -1 and c = 0
So, π1 = ω•b^a•v^b•ρ^c.
π1 = ω•b^1•v^-1•ρ^0
π1 = ω•b / v
Check dimensions
ωb/v = (T^-1)L / LT^-1 = L^0•T^0 = 1
Then, π1 is dimensionless
For second pi
π2 = h•b^a•v^b•ρ^c.
Since
h = L, b = L, v = LT^-1 and ρ= FL^-4T²
Since π is dimensionless then,
π = F^0•L^0•T^0
(L)•(L^a)•(LT^-1)^b•(FL^-4T²)^c = F^0•L^0•T^0
Rearranging
F^0•L^0•T^0 = F^c•T^(2c-b)• L^(1+a+b-4c)
Comparing coefficient
c = 0
2c - b = 0
b = 2c = 0
1 + a + b - 4c = 0
a = 4c - b - 1 = 0 -0 - 1 = -1
a = -1
Then, a = -1, b = 0 and c = 0
So, π2 = h•b^a•v^b•ρ^c.
π2 = h•b^-1•v^0•ρ^0
π2 = h / b
Check dimensions
h / b = L / L = 1
Then, π2 is dimensionless
For third pi
π3 = k•b^a•v^b•ρ^c.
Since
k= FL, b = L, v = LT^-1 and ρ=FL^-4T²
Since π is dimensionless then,
π = F^0•L^0•T^0
(FL)•(L^a)•(LT^-1)^b•(FL^-4T²)^c = F^0•L^0•T^0
Rearranging
F^0•L^0•T^0 = F^(c+1)•T^(2c-b)• L^(1+a+b-4c)
Comparing coefficient
c + 1= 0
Then, c = -1
2c - b = 0
b = 2c = -2
1 + a + b - 4c = 0
a = 4c - b - 1 = -4 +2 - 1 = -3
a = -3
Then, a = -3, b = -2 and c = -1
So, π3 = k•b^a•v^b•ρ^c.
π3 = k•b^-3•v^-2•ρ^-1
Therefore,
π3 = k / b³•v²•ρ
Let check for dimension
π3 = FL / (L³• L²T^-2 • FL^-4T²)
π3 = FL / (L^(3+2-4) • T^(-2+2) •F)
π3 = FL / (L• T^(0) •F)
π3 = FL / LF = 1
π3 is also dimensions less
So.
I. There are three none dimensional pi
II. The none dimensional group are
π1 = ω•b / v
π2 = h / b
π3 = k / b³•v²•ρ
III. Reynolds Number. The Reynolds number is the ratio of inertial forces to viscous forces and it is dimensionless
So, the π3 can be considered as a Reynolds number
