Answer:
A) Volume flow rate = 0.0327 ft³/s; mass flow rate = 2.04 lb/s
B) 81.96 seconds
C) 37.77 ft/s
Explanation:
A) The formula for the volume flow rate is;
V' = Av
Where A is the area and v is the velocity.
Area = πD²/4
From the question, D(diameter) = 1 inch. So let's convert it to ft since the velocity is in ft.
Thus, 1 inch = 0.0833 ft
Thus Area(A) = π(0.0833)²/4 = 0.00545 ft²
So, V' = 0.00545 x 6 = 0.0327 ft³/s
The mass flow rate is calculated as;
m' = ρv
Where, ρ = density.
Density of water in lb/ft³ = 62.4 lbs/ft³
Thus mass flow rate (m') = 62.4 x 0.00327 = 2.04 lb/s
B) The time it will take to fill the bucket is gotten from the formula;
t = V/V'
From the question, V = 20 gallons
Converting this to ft³, we have;
Since, 1 gallon = 0.134 ft³
20 gallons = 20 x 0.134 = 2.68 ft³
So, t = 2.68/0.0327 = 81.96 seconds
C) The velocity at the outlet is gotten from the formula;
v2 = v1((D1)²/(D2)²)
Since the diameter reduces to 0.4 inches at the exit, D2 = 0.4inches = 0.0332
Thus; v2 = 6(0.0833²/0.0332²) = 37.77 ft/s