Answer:
See attachment and explanation.
Explanation:
- The following question can be solved better with the help of a MATLAB program as follows. The code is given in the attachment.
- The plot of the graph is given in attachment.
- The code covers the entire spectrum of the poly-tropic range ( 1.2 - 1.6 ) and 20 steps ( cases ) have been plotted and compared in the attached plot.
Answer:
The expression is shown in the explanation below:
Explanation:
Thinking process:
Let the time period of a simple pendulum be given by the expression:
Let the fundamental units be mass= M, time = t, length = L
Then the equation will be in the form
where k is the constant of proportionality.
Now putting the dimensional formula:
Equating the powers gives:
a = 0
b + c = 0
2c = 1, c = -1/2
b = 1/2
so;
a = 0 , b = 1/2 , c = -1/2
Therefore:
T =
where k =
Answer:
a) 1.16 m/s
b) 1/216000
c) (√15)/6480000
Explanation:
The parameters given are;
Length of boat prototype, lp = 30 m
Speed of boat prototype = 9 m/s
Length of boat model, lm= 0.5 m
a) lm/lp = 0.5/30 = 1/60 = ∝
(vm/vp) = ∝^(1/2) = √∝ = (1/60)^(1/2)
vm = 9 × (1/60)^(1/2) = 1.16 m/s
b) The ratio of the model to prototype drag, Fm/Fp, is given as follows;
Fm/Fp = (vm/vp)²×(lm/lp)² = ∝³
Fm/Fp = (1/60)³ = 1/216000
c) The ratio of the model to prototype power pm/p = (Fm/Fp) × (vm/vp) = ∝³×√∝
The ratio of the model to prototype power pm/p = √(1/60) × (1/60)³
pm/p = √(1/60) × (1/60)³ = (√15)/6480000