Help with Bernoulli's Equation

In summary, the gauge pressure and speed of a horizontal fire hose of diameter 5.4 cm and a metal tip of diameter 2.5 cm are calculated using the Volumetric Flow rate equation and the formula for constant pressure. The resulting pressure is 133,716 N/m^2.
  • #1
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Homework Statement



The gauge pressure in a horizontal fire hose of diameter 5.4 cm is 3.0 x 105 Nm-2 and the speed of flow is 4.0 ms-1. The fire hose ends in a metal tip of diameter 2.5 cm. What are the pressure and the speed of the water in the tip?

Homework Equations




P+ρgh+0.5ρv^2=Constant
Volumetric Flow rate = A*v
Mass Flow Rate = ρ*Volumetric Flow rate

The Attempt at a Solution



Volumetric Flow rate = 0.00229*4 = 0.00916m3/s
Speed at end of hose = 0.00916/0.000491 = 18.67m/s

300000 + (0.5*1000*4^2) = P2 + (0.5*1000*18.67)
= 308000 = P2+174845

∴ P2 = 308000-17845 = 133155Pascals or 1.3 Bar

I am just checking this is right. As this is the answer I keep getting but the tutorial answers show something different.
 
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  • #2
You have to square the 18.67. Check your arithmetic. I get 133,716 N/m^2.

AM
 
Last edited:

Related to Help with Bernoulli's Equation

1. What is Bernoulli's Equation?

Bernoulli's Equation is a fundamental principle in fluid dynamics that relates the pressure, velocity, and height of a fluid.

2. How is Bernoulli's Equation used in real-world applications?

Bernoulli's Equation is used in a wide range of applications, such as designing airplane wings, calculating the flow of fluids in pipes, and understanding weather patterns.

3. What is the formula for Bernoulli's Equation?

The formula for Bernoulli's Equation is P1 + 1/2ρv1^2 + ρgh1 = P2 + 1/2ρv2^2 + ρgh2, where P is pressure, ρ is density, v is velocity, and h is height.

4. How does Bernoulli's Equation relate to the conservation of energy?

Bernoulli's Equation is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In the case of Bernoulli's Equation, it shows how the energy of a fluid is conserved as it moves from one point to another.

5. What are some common misconceptions about Bernoulli's Equation?

One common misconception is that Bernoulli's Equation applies only to ideal fluids, when in fact it can be applied to real fluids as well. Another misconception is that Bernoulli's Equation only applies to steady, incompressible flow, but it can also be used for unsteady and compressible flow with some modifications.

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