HELP _7. All of the following except which would lead to an INCREASE in friction?
1 answer:
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Answer:
The solution and explanation is attached.
Explanation:
Answer:
12 mins
Explanation:
The summation of the forces in vertical direction
= Fb - Fd - w = 0 ∴ Fd = Fb - w ----- ( 1 )
Fb ( buoyant force ) = Pair * g * Vballoon ------- ( 2 )
Pair = air density , Vballoon = volume of balloon
Vballoon = , where D = 4 ∴ Vballoon = 33.51 ft^3
g = 32.2 ft/s^2
From property tables
Pair = 2.33 * 10^-3 slug/ft^3
μ ( dynamic viscosity ) = 3.8 * 10^-7 slug/ft.s
<em>Insert values into equation 2 </em>
Fb = ( 2.33 * 10^-3 ) * ( 32.2 ) *( 33.51 ) = 2.514 Ib
∴ Fd = 2.514 - 2.5 = 0.014 Ib ( equation 1 )
Assuming that flow is Laminar and RE < 1
Re = (Pair * vd) / μair -------- ( 3 )
where: Pair = 2.33 * 10^-3 slug/ft^3 , vd = ( 987 * 4 ) ft^2/s , μair = 3.8 * 10^-7 slug/ft.s
Insert values into equation 3
Re = 2.4 * 10^7 ( this means that the assumption above is wrong )
Hence we will use drag force law
Assume Cd = 0.5
Express Fd using the relation below
Fd = 1/2* Cd * Pair * AV^2
therefore V = 1.39 ft/s
Recalculate Reynold's number using v = 1.39 ft/s
Re = 34091
from the figure Cd ≈ 0.5 at Re = 34091
<u>Finally calculate the rise time ( time taken to reach an altitude of 1000 ft ) </u>
t = h/v
= 1000 / 1.39 = 719 seconds ≈ 12 mins
