Water flowing out of a horizontal pipe emerges through a nozzle. The radius of the pipe is 1.8 cm, and the radius of the nozzle is 0.53 cm. The speed of the water in the pipe is 0.75 m/s. Treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe.

The absolute pressure of the water in the pipe is 1.38 x 10⁵ Pa

Explanation:

Given;

radius of the pipe, r₁ = 1.8 cm = 0.018 m

radius of the pipe, r₂ = 0.53 cm = 0.0053 m

speed of water in the pipe, v₁ = 0.75 m/s

Water absolute pressure can be determined using Bernoulli's equation;

P₁ + ¹/₂ρv₁² = P₂ + ¹/₂ρv₂²

P₁ =  P₂ + ¹/₂ρv₂² - ¹/₂ρv₁²

P₁ =  P₂ + ¹/₂ρ (v₂² - v₁²)

where;

ρ is density of water = 1000 kg/m³

P₂  is atmospheric pressure = 1.01 x 10⁵ Pa

From continuity equation; A₁V₁ = A₂V₂

πr₁²v₁² = πr₂²v₂²

Therefore, the absolute pressure of the water in the pipe is 1.38 x 10⁵ Pa