The pressure in the hose as the speed of water changes from 2.05 m/s to 31.4 m/s as it goes through the nozzle is 5.92 × 10⁵ N/m².
Given:
The flow of water through the hose initially, v₁ = 2.05 m/s
The flow of water through the hose initially, v₂ = 31.4 m/s
Calculation:
From Bernoulli's equation we have:
P₁ + 1/2 ρv₁² + ρgh₁ = P₂ + 1/2 ρv₂² + ρgh₂
where P₁ is atmospheric pressure
P₂ is the pressure in the hose
ρ is the density of the fluid
h₁ is the initial height
h₂ is the final height
v₁ is the initial velocity of the fluid
v₂ is the final velocity of the fluid and
g is the acceleration due to gravity
Re-arranging the above equation we get:
P₂ = P₁ + 1/2 ρ(v₁²-v₂²) + ρg (h₁-h₂)
Applying values in the above equation we get:
P₂ = P₁ + 1/2 ρ(v₁²-v₂²) + ρg (0)
= (1.01 × 10⁵ Pa)+ 1/2 (10³ g/m³) [(31.4m/s)²-(2.05 m/s)²]
= (1.01 × 10⁵ Pa)+ 1/2 (10³ g/m³) [981.7575]
= (1.01 × 10⁵ Pa)+ (4.91 × 10⁵ Pa)
= 5.92 × 10⁵ Pa
= 5.92 × 10⁵ N/m²
Therefore, the pressure in the hose is 5.92 × 10⁵ N/m².
Learn more about Bernoulli's equation here:
<u>brainly.com/question/9506577</u>
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