Given:
diameter of sphere, d = 6 inches
radius of sphere, r = 
= 3 inches
density, 
= 493 lbm/ 
S.G = 1.0027
g = 9.8 m/ 
= 386.22 inch/ 
Solution:
Using the formula for terminal velocity,
= 
(1)
where,
V = volume of sphere
= drag coefficient
Now,
Surface area of sphere, A = 
Volume of sphere, V = 
Using the above formulae in eqn (1):
= 
= 
= 
Therefore, terminal velcity is given by:
= 
inch/sec
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Explanation: See above.
I hope this helps.
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Answer
No;
The two flows are not dynamically similar
Explanation: Given
T∞,1 = 800k
V∞,1 = 200m/s
p∞,1 = 1.739kg/m³
T∞,2 = 200k
V∞,2 = 100m/s
p∞,2 = 1.23kg/m³
Size1 = 2 * Size2 (L1 = 2L2) Assumptions Made
α ∝√T
μ∝√T Two (2) conditions must be met if the two flows are to be considered similar.
Condition 1: Similar Parameters must be the same for both flows
Condition 2: The bodies and boundaries must be genetically true. Condition 2 is true
Checking for the first condition...
Well need to calculate Reynold's Number for both flows
And Check if they have the same Reynold's Number Using the following formula
Re = pVl/μ
Re1 = p1V1l1/μ1 Re2 = p2V2l2/μ2 Re1/Re2 = p1V1l1/μ1 ÷ p2V2l2/μ2
Re1/Re2 = p1V1l1/μ1 * μ2/p2V2l2
Re1/Re2 = p1V1l1μ2/p2V2l2μ1
Re1/Re2 = p1V1l1√T2 / p1V1l1√T1
Re1/Re2 = (1.739 * 200 * 2L2 * √200) / (1.23 * 100 * L2 * √800)
Re1/Re2 = 9837.2/3479
Re1/Re2 = 2,828/1
Re1:Re2 = 2.828:1
Re1 ≠ Re2,
So condition 1 is not satisfied Since one of tbe conditions is not true, the two flows are not dynamically similar
