Question

Water is flowing down through the pipe shown in the drawing. Point A is 0.410 m higher than B. The speed of the water at A and B are vA = 5.00 m/s and vB = 2.78 m/s. Determine the difference PB - PA in pressures between B and A. The density of water is 1.00 × 103 kg/m3.

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Answer 1

Answer on Question#37655, Physics, Other

Question:

Water is flowing down through the pipe shown in the drawing. Point A is 0.410 m higher than B. The speed of the water at A and B are vA = 5.00 m/s and vB = 2.78 m/s. Determine the difference PB - PA in pressures between B and A. The density of water is 1.00 × 10³ kg/m³.

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Answer:

Bernoulli's principle can be expressed as a mathematical equation:

$$\frac {v ^ {2}}{2} + g h + \frac {p}{\rho} = c o n s t$$

where $v$ is the water streams speed, $g$ is the acceleration due to gravity, $h$ is the height, $p$ is the pressure, and $\rho$ is the density of the water.

In our case:

$$\frac {v _ {A} ^ {2}}{2} + g h _ {A} + \frac {p _ {A}}{\rho} = \frac {v _ {B} ^ {2}}{2} + g h _ {B} + \frac {p _ {B}}{\rho}$$

Therefore:

$$p _ {B} - p _ {A} = \rho \left(\frac {v _ {A} ^ {2}}{2} - \frac {v _ {B} ^ {2}}{2} + g (h _ {A} - h _ {B})\right) = 1 2 7 0 0 P a = 1 2. 7 k P a$$

Answer: 12.7 kPa