**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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