Answer:
velocity = 472 m/s
velocity = 52.4 m/s
Explanation:
given data
steady rate = 0.750 m³/s
diameter = 4.50 cm
solution
we use here flow rate formula that is
flow rate = Area × velocity .............1
0.750 = [tex]\frac{\pi }{4}[/tex] × (4.50×[tex]10^{-2}[/tex])² × velocity
solve it we get
velocity = 472 m/s
and
when it 3 time diameter
put valuer in equation 1
0.750 = [tex]\frac{\pi }{4}[/tex] × 3 × (4.50×[tex]10^{-2}[/tex])² × velocity
velocity = 52.4 m/s
This question involves the concepts of the volume flow rate and the flow velocity.
(a) It will shoot out of a hole 4.50 cm in diameter with a flow velocity of "471.6 m/s".
(b) It will shoot out of the diameter of the hole is three times as large with a flow velocity of "52.4 m/s".
(a)
The volume flow rate is given by the following formula:
[tex]V=Av\\\\v=\frac{V}{A}[/tex]
where,
V = volume flow rate = 0.75 m³/s
A = Area of hole = [tex]\pi \frac{d^2}{4}=\pi \frac{(0.045\ m)^2}{4}=0.0016\ m^2[/tex]
[tex]v[/tex] = flow velocity = ?
[tex]v=\frac{0.75\ m^3/s}{0.0016\ m^2}\\\\v = 471.6\ m/s[/tex]
(b)
The volume flow rate is given by the following formula:
[tex]V=Av\\\\v=\frac{V}{A}[/tex]
where,
V = volume flow rate = 0.75 m³/s
A = Area of hole = [tex]\pi \frac{d^2}{4}=\pi \frac{(3*0.045\ m)^2}{4}=0.0143\ m^2[/tex]
[tex]v[/tex] = flow velocity = ?
[tex]v=\frac{0.75\ m^3/s}{0.0143\ m^2}\\\\v = 52.4\ m/s[/tex]
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