Question

Water flowing out of a horizontal pipe emerges through a nozzle. The radius of the pipe is 2.3 cm, and the radius of the nozzle is 0.41 cm. The speed of the water in the pipe is 0.74 m/s. Treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe.

Answer 1

Ans)

The absolute pressure in the pipe must be greater than the atmospheric pressure.

According to bernoulli’s equation,

P₁+(1/2)?v₁² +?gy₁= P₂+(1/2)?v₂² +?gy₂

      pipe                       nozzle

the pipe and nozzle are horizontal ,so that y₁=y₂ then the above equation comes to

P₁+(1/2)?v₁² = P₂+(1/2)?v₂²

Where p1 is the absolute pressure of the water in the pipe.

Therefore P₁= P₂+(1/2)?(v₂² –v₁²)

By equation of continuity we know that

v₂=r₁²v₁²/r₂²

P₁= P₂+(1/2)?((r₁⁴/r₂⁴)-1)v₁²

Density of water ?=1.00x10³ kg/m³

P₁=(1.01x10⁵)+(1/2)(1x10³)[(2.3/0.41)⁴-1]x(0.74)²

=101000+270876.035

P₁=3.72x10⁵ pa