Water flows flows through the lower segment of a pipe with a cross sectional are

Question

Water flows flows through the lower segment of a pipe with a cross sectional area of 0.12 m^2 at a velocity of 2 m/s. It then flows up another pipe to the upper segment of the pipe, 3m above the lower segment. The upper segment has a cross sectional area of 0.030 m^2. What is the difference in water pressure between the two pipe segment? In which segment is the pressure greater? Assume density of water is 1000 kg/m^3 Water flows flows through the lower segment of a pipe with a cross sectional area of 0.12 m^2 at a velocity of 2 m/s. It then flows up another pipe to the upper segment of the pipe, 3m above the lower segment. The upper segment has a cross sectional area of 0.030 m^2. What is the difference in water pressure between the two pipe segment? In which segment is the pressure greater? Assume density of water is 1000 kg/m^3

Explanation / Answer

Here ,

area of lower segment , A1 = 0.12 m^2

area of upper segment , A2 = 0.030 m^2

velocity in lower segment , v1 = 2 m/s

velocity of upper circuit is v2

Using equation of continuity

v1 * A1 = v2 * A2

0.12 * 2 = v2 * 0.03

v2 = 8 m/s

Now , for the difference in pressure ,

P = p * g * h + 0.5 * p * (v2^2 - v1^2)

P = 1000 * (9.8 * 3 + 0.5 * (8^2 - 2^2))

P = 59400 Pa

the pressure differnce is 59400 Pa

the pressure in the lower segment will be higher

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