Respuesta :
Answer:
the highest possible average flow velocity is 17 m/s
Explanation:
given data
power = 60 W
pressure = 50 Pa
diameter = 30 cm = 0.3 m
to find out
Determine the highest possible average flow velocity in the duct
solution
we will apply here energy balance equation that is
energy in = energy out
power + m(Pv)1 = m (Pv)2
power = mv ( P2 -P1)
power = V ΔP
here P is pressure and V is maximum volume flow rate
put here value and find V
60 = V ( 50)
maximum volume v = 1.2 m³/s
and
maximum average velocity is
Velocity = [tex]\frac{V}{\frac{\pi }{4} D^2 }[/tex]
here D is diameter and V is volume
so
velocity = [tex]\frac{1.2}{\frac{\pi }{4} 0.3^2 }[/tex]
velocity = 17 m/s
so the highest possible average flow velocity is 17 m/s
The highest possible average flow velocity in the duct is 17 m/s
Energy balance equation:
Here we applied the above equation i.e.
energy in = energy out
power + m(Pv)1 = m (Pv)2
power = mv ( P2 -P1)
power = V ΔP
where,
P is pressure and V is maximum volume flow rate
Now V should be
60 = V ( 50)
So, maximum volume v = 1.2 m³/s
Now the maximum velocity should be
[tex]= 1.2 \div (\pi \div 4 (0.3)^2)[/tex]
= 17 m/s
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