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maw [93]
2 years ago
9

Consult Multiple-Concept Example 15 to review the concepts on which this problem depends. Water flowing out of a horizontal pipe

emerges through a nozzle. The radius of the pipe is 1.8 cm, and the radius of the nozzle is 0.49 cm. The speed of the water in the pipe is 0.56 m/s. Treat the water as an ideal fluid, and determine the absolute pressure of the water in the pipe. (The atmosphere pressure is P = 1.01 105 Pa, and the density of water is rho = 1.00 103 kg/m3.)
Physics
1 answer:
kiruha [24]2 years ago
3 0

Answer:

The pressure of the water in the pipe is 129554 Pa.

Explanation:

<em>There are wrongly written values on the proposal, the atmospheric pressure must be 101105 Pa, and the density of water 1001.03 kg/m3, those values are the ones that make sense with the known ones.</em>

We start usign the continuity equation, and always considering point 1 a point inside the pipe and point 2 a point in the nozzle:

A_1v_1=A_2v_2

We want v_2, and take into account that the areas are circular:

v_2=\frac{A_1v_1}{A_2}=\frac{\pi r_1^2 v_1}{\pi r_2^2}=\frac{r_1^2 v_1}{r_2^2}

Substituting values we have (we don't need to convert the cm because they cancel out between them anyway):

v_2=\frac{r_1^2 v_1}{r_2^2}=\frac{(1.8cm)^2 (0.56m/s)}{(0.49cm)^2}=7.56m/s

For determining the absolute pressure of the water in the pipe we use the Bernoulli equation:

P_1+\frac{\rho v_1^2}{2}+\rho gh_1=P_2+\frac{\rho v_2^2}{2}+\rho gh_2

Since the tube is horizontal h_1=h_2 and those terms cancel out, so the pressure of the water in the pipe will be:

P_1=P_2+\frac{\rho v_2^2}{2}-\frac{\rho v_1^2}{2}=P_2+\frac{\rho (v_2^2-v_1^2)}{2}

And substituting for the values we have, considering the pressure in the nozzle is the atmosphere pressure since it is exposed to it we obtain:

P_1=101105 Pa+\frac{1001.03Kg/m^3 ((7.56m/s)^2-(0.56m/2)^2)}{2}=129554 Pa

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