Respuesta :
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
In the given case,
(a) the volume and mass flow rates of water through the hose = 0.0327 ft³/s and 2.04 lb/s
(b) how long it will take to fill the bucket with water = 81.96 seconds
(c) the average velocity of water at the nozzle exit - 37.77 ft/s
Given:
D (diameter) = 1 inch.
1 inch = 0.0833 ft ...1
V = 20 gallons
1 gallon = 0.134 ft³
20 gallons = 20 x 0.134 = 2.68 ft³ ....2
D2 = 0.4inches = 0.0332 .... 3
A) The formula for the volume flow rate is;
V’ = Av
Where A is the area and v is the velocity.
Area = [tex]\frac{\pi D^2}{4}[/tex]
(A) = [tex]\frac{\pi (0.0833)^2}{4}[/tex] (from 1)
= 0.00545 ft²
So,
V’ = 0.00545 x 6
= 0.0327 ft³/s
The mass flow rate:
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:
t = V/V’
So, t =[tex]\frac{2.68}{0.0327}[/tex] (from 2)
= 81.96 seconds
C) The velocity at the outlet is gotten:
v2 = [tex]v1(\frac{D1^2}{D2^2})[/tex]
v2 =[tex]6(\frac{0.0833^2}{0.0332^2})[/tex] ( from 3)
= 37.77 ft/s
Thus, In the given case,
(a) the volume and mass flow rates of water through the hose = 0.0327 ft³/s and 2.04 lb/s
(b) how long it will take to fill the bucket with water = 81.96 seconds
(c) the average velocity of water at the nozzle exit - 37.77 ft/s
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