Question

Water flows through a pipe that gradually descends from a height of 6.78 m to the ground. Near the top, the cross-sectional area is 0.4 m², and the pipe gradually widens so that its area near the ground is 0.8 m². Water leaves the pipe at a speed of 16.8 m/s. What is the difference in the water pressure between the top and bottom of the pipe?

Answer 1

Solution:

Given:

A₁ = 0.4 m²

A₂ = 0.8 m²

v₂ = 16.8 m/s

h = 6.78 m

According to Continuity principle: A₁ v₁ = A₂ v₂

Therefore: speed at the top (v₁) = (0.8)(16.8/0.40) = 33.6 m/s

Now, Using Bernoulli's equation:

(0.5)(1000)(33.6)² + (1000)(9.8)(6.78) + P₁ = (0.5)(1000)(16.8)² + P₂

630924 + P₁ = 14110 + P₂

P₂ - P₁ = 489804 Pa

Therefore: the difference in the water pressure between the top and bottom of the pipe is 489804 Pa