A) Speed in the lower section: 0.638 m/s
B) Speed in the higher section: 2.55 m/s
C) Volume flow rate:
Explanation:
A)
To solve the problem, we can use Bernoulli's equation, which states that
where
is the pressure in the lower section of the tube
is the heigth of the lower section
is the density of water
is the acceleration of gravity
is the speed of the water in the lower pipe
is the pressure in the higher section
is the height in the higher pipe
is hte speed in the higher section
We can re-write the equation as
(1)
Also we can use the continuity equation, which state that the volume flow rate is constant:
where
is the cross-section of the lower pipe, with
is the radius of the lower pipe (half the diameter)
is the cross-section of the higher pipe, with
(radius of the higher pipe)
So we get
And so
(2)
Substituting into (1), we find the speed in the lower section:
B)
Now we can use equation (2) to find the speed in the lower section:
Substituting
v1 = 0.775 m/s
And the values of the radii, we find:
C)
The volume flow rate of the water passing through the pipe is given by
where
A is the cross-sectional area
v is the speed of the water
We can take any point along the pipe since the volume flow rate is constant, so
Therefore, the volume flow rate is
Learn more about pressure in a liquid:
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