Answer: Attached below is the well written question and solution
answer:
i) Attached below
ii) similar parameter = 
Explanation:
Using ; L as characteristic length and Vo as reference velocity
i) Nondimensionalize the equations
ii) Identifying similarity parameters
the similar parameters are = 
Attached below is the detailed solution
Answer:

Explanation:
the half life of the given circuit is given by

where [/tex]\tau = RC[/tex]

Given 
resistance in the circuit is 40 ohm and to extend the half cycle we added new resister of 48 ohm. the net resitance is 40+48 = 88 ohms
now the new half life is

Divide equation 2 by 1


putting all value we get new half life


The pressure of water is 7.3851 kPa
<u>Explanation:</u>
Given data,
V = 150×

m = 1 Kg
= 2 MPa
= 40°C
The waters specific volume is calculated:
= V/m
Here, the waters specific volume at initial condition is
, the containers volume is V, waters mass is m.
= 150×
/1
= 0.15
/ Kg
The temperature from super heated water tables used in interpolation method between the lower and upper limit for the specific volume corresponds 0.15
/ Kg and 0.13
/ Kg.
= 350+(400-350) 
= 395.17°C
Hence, the initial temperature is 395.17°C.
The volume is constant in the rigid container.
=
= 0.15
/ Kg
In saturated water labels for
= 40°C.
= 0.001008
/ Kg
= 19.515
/ Kg
The final state is two phase region
<
<
.
In saturated water labels for
= 40°C.
=
= 7.3851 kPa
= 7.3851 kPa
Answer: r = 0.8081; s = -0.07071
Explanation:
A = (150i + 270j) mm
B = (300i - 450j) mm
C = (-100i - 250j) mm
R = rA + sB + C = 0i + 0j
R = r(150i + 270j) + s(300i - 450j) + (-100i - 250j) = 0i + 0j
R = (150r + 300s - 100)i + (270r - 450s - 250)j = 0i + 0j
Equating the i and j components;
150r + 300s - 100 = 0
270r - 450s - 250 = 0
150r + 300s = 100
270r - 450s = 250
solving simultaneously,
r = 0.8081 and s = -0.07071
QED!