Plan, design, and implement solar energy projects
Answer:
Given that

LHS of above given equation have dimension
.
Now find the dimension of RHS
Dimension of P =
.
Dimension of d=
.
Dimension of μ =
.
Dimension of L=
.
So
![\dfrac{\Delta Pd^2}{32\mu L}=\dfrac{[ML^{-1}T^{-2}].[M^{0}L^{1}T^{0}]^2}{[ML^{-1}T^{-1}].[M^{0}L^{1}T^{0}]}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5CDelta%20Pd%5E2%7D%7B32%5Cmu%20L%7D%3D%5Cdfrac%7B%5BML%5E%7B-1%7DT%5E%7B-2%7D%5D.%5BM%5E%7B0%7DL%5E%7B1%7DT%5E%7B0%7D%5D%5E2%7D%7B%5BML%5E%7B-1%7DT%5E%7B-1%7D%5D.%5BM%5E%7B0%7DL%5E%7B1%7DT%5E%7B0%7D%5D%7D)
![\dfrac{\Delta Pd^2}{32\mu L}=[M^0L^{1}T^{-1}]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5CDelta%20Pd%5E2%7D%7B32%5Cmu%20L%7D%3D%5BM%5E0L%5E%7B1%7DT%5E%7B-1%7D%5D)
It means that both sides have same dimensions.
Answer:
The correct answers are:
a. % w = 33.3%
b. mass of water = 45g
Explanation:
First, let us define the parameters in the question:
void ratio e =
= 
Specific gravity
=

% Saturation S =
×
=
× 
water content w =
=
a) To calculate the lower and upper limits of water content:
when S = 100%, it means that the soil is fully saturated and this will give the upper limit of water content.
when S < 100%, the soil is partially saturated, and this will give the lower limit of water content.
Note; S = 0% means that the soil is perfectly dry. Hence, when s = 1 will give the lowest limit of water content.
To get the relationship between water content and saturation, we will manipulate the equations above;
w = 
Recall; mass = Density × volume
w = 
From eqn. (2)
= 
∴ 
putting eqn. (6) into (5)
w = 
Again, from eqn (1)

substituting into eqn. (7)

∴ 
With eqn. (7), we can calculate
upper limit of water content
when S = 100% = 1
Given, 
∴
∴ %w = 33.3%
Lower limit of water content
when S = 1% = 0.01

∴ % w = 0.33%
b) Calculating mass of water in 100 cm³ sample of soil (
)
Given,
, S = 50% = 0.5
%S =
×
=
× 
0.50 = 
mass of water = 