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34) water is flowing at a rate of 2m3/s through a tube with a diameter of 1m. if the pressure at this point is 80kpa, what is the pressure of the water after the tube narrows to a diameter of 0.5m?

Respuesta :

Eduard22sly

The pressure of the water after the tube narrows to a diameter of 0.5 m is 320.4 KPa

How do I determine the pressure?

We know that pressure is defined as:

Pressure (P) = Force (F) / Area (A)

P = F / A

If F is constant, then we have

P₁A₁ = P₂A₂

Where

  • P₁ and P₂ are the Initial and new pressure
  • A₁ and A₂ are the Initial and new area

With the above formula, we can obtain the new pressure as follow:

  • Initial pressure (P₁) = 80 KPa
  • Pi (π) = 3.14
  • Initial diameter (d₁) = 1 m
  • Initial area (A₁) = π(d₁ / 2)² = 3.14 × (1 / 2)² = 0.785 m²
  • New diameter (d₂) = 0.5 m
  • New area (A₂) = π(d₂ / 2)² = 3.14 × (0.5 / 2)² = 0.196 m²
  • New pressure (P₂) = ?

From the above data, we can obtain the new pressure as illustrated below:

P₁A₁ = P₂A₂

Divide both sides by A₂

P₂ = P₁A₁ / A₂

P₂ = (80 × 0.785) / 0.196

P₂ = 320.4 KPa

Thus, we can conclude that the pressure is 320.4 KPa

Learn more about pressure:

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