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Water flowing through a 10-cm-diameter water pipe at a rate of 0.1 m3/s. Now a diffuser with an outlet diameter of 20 cm is bolted to the pipe in order to slow down water. The inlet side of the pipe is part of a continuous piping system( so that the pressure may not be atmospheric), but the outlet is discharging water to the atmosphere. Disregarding the frictional effects, determine the force exerted on the bolts due to the water flow?







I saw many answers and they solve for Bernoulli equation and they find the gage pressure to be positive and the final answer to be 1551N. and I solve for gage pressure to be negative and find the last answer to be 364.3 N







which one is correct?

Respuesta :

Answer:

yours

Explanation:

onyebuchinnaji

The force exerted on the bolts due to the water flow is determined as 1,790 N.

Inlet velocity of the water

Q = Av

where;

  • Q is volumetric flow rate
  • v is inlet velocity

v = Q/A

v₁ = (0.1)/(π x 0.05²)

v₁ = 12.73 m/s

Outlet velocity of the water

A₁v₁ = A₂v₂

πr₁²v₁ = πr₂²v₂

r₁²v₁ = r₂²v₂

v₂ = (r₁²v₁)/(r₂²)

v₂ = (0.05² x 12.73)/(0.1²)

v₂ = 3.18 m/s

Gauge pressure

Apply Bernoulli's equation

P₂ - P₁ = ¹/₂ρ(v₂² - v₁²) + ρg(h₂ - h₁)

P₂ - P₁ = ¹/₂ρ(v₁² - v₂²) + ρg(0)

P₂ - P₁ = ¹/₂ρ(v₁² - v₂²)

P₂ - P₁ = ¹/₂ x 1000 x (12.73² - 3.18²)

P₂ - P₁ = 75,970.25 Pa

Force exerted on the bolts

F = PA

F = 75,970.25 x π(0.1² - 0.05²)

F = 1,790 N

Learn more about gauge pressure here: https://brainly.com/question/6984092

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