a horizontal pipe with a diameter of 3 cm narrows down to a diameter of 2 cm, where it expels water into the surrounding air at a speed of 32 m/s. what is the gauge pressure in the larger diameter section of the pipe?

Answers

Answer 1

A horizontal pipe with a 3 cm diameter that narrows to a 2 cm diameter at a speed of 32 m/s releases water into the air around it. The pipe's larger diameter section's gauge pressure is 512,000 Pa.

To determine the gauge pressure in the larger diameter section of the pipe, we can apply Bernoulli's principle, which states that the total pressure at any point in a fluid system is the sum of the static pressure and the dynamic pressure.

Given:

Diameter of the larger section (D1) = 3 cm = 0.03 m

Diameter of the smaller section (D2) = 2 cm = 0.02 m

Velocity of water (v) = 32 m/s

We'll assume the flow is steady and the fluid is incompressible. The density of water (ρ) is approximately 1000 kg/m³.

Using Bernoulli's principle, we have:

[tex]P_1 + \frac{1}{2}\rho v_1^2 = P_2 + \frac{1}{2}\rho v_2^2[/tex]

Since the larger section of the pipe has a larger diameter, we can assume it has a lower velocity compared to the smaller section.

[tex]P_1 + \frac{1}{2}\rho v_1^2 > P_2 + \frac{1}{2}\rho v_2^2[/tex]

The gauge pressure (P1) in the larger diameter section can be calculated as follows:

[tex]P_1 = P_2 + \frac{1}{2}\rho(v_2^2 - v_1^2)[/tex]

[tex]P_1 = P_2 + \frac{1}{2}\rho(v_2 + v_1)(v_2 - v_1)[/tex]

Since the pipe is open to the surrounding air, we can assume atmospheric pressure (P2) is present in the smaller diameter section.

P2 = 0 (gauge pressure at atmospheric pressure)

Therefore, the gauge pressure in the larger diameter section (P1) is:

[tex]P_1 = \frac{1}{2}\rho(v_2 + v_1)(v_2 - v_1)[/tex]

Plugging in the values, we get:

[tex]P1 = \frac{1}{2} \times 1000 , \text{kg/m}^3 \times (32 , \text{m/s} + 0 , \text{m/s}) \times (32 , \text{m/s} - 0 , \text{m/s})[/tex]

Calculating the expression, we find:

P1 = 512,000 Pa

Therefore, the gauge pressure in the larger diameter section of the pipe is 512,000 Pa.

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Correct question is;

2, A rectangular Container of base 50 cm by 30cm is filled with water to be depth of 5cm. how much is the pressure exerted at the base? (take pw= 1000kg /m3 and g=10m/s)​

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Rudolf Virchow

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