Question

Water (rhoH20 = 1000.0 kg/m3 ) flows through a garden hose that goes up a step 20.0 cm high. The cross-sectional area of the hose on the top of the step is half that at the bottom of the step. The speed of the water at the bottom of the step is 1.20 m/s. If the water pressure is 143 kPa at the bottom of the step, what is the water pressure at the top of the step?

Answer 1

P₂ = 138.88 10³ Pa

Step-by-step explanation:

This is a problem of fluid mechanics, we must use the continuity and Bernoulli equation

Let's start by looking for the top speed

Q = A₁ v₁ = A₂ v₂

We will use index 1 for the lower part and index 2 for the upper part, let's look for the speed in the upper part (v2)

v₂ = A₁ / A₂ v₁

They indicate that A₂ = ½ A₁ and give the speed at the bottom (v₁ = 1.20 m/s)

v₂ = 2 1.20

v₂ = 2.40 m / s

Now let's write the Bernoulli equation

P₁ + ½ ρ v₁² + ρ g y₁ = P2 + ½ ρ v₂² + ρ g y₂

Let's clear the pressure at point 2

P₂ = P₁ + ½ ρ (v₁² - v₂²) + ρ g (y₁-y₂)

we put our reference system at the lowest point

y₁ - y₂ = -20 cm

Let's calculate

P₂ = 143 10³ + ½ 1000 (1.20² - 2.40²) + 1000 9.8 (-0.200)

P₂ = 143 103 - 2,160 103 - 1,960 103

P₂ = 138.88 10³ Pa