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A water pipe having a 2.5cminside diameter carries water into the basement of a house at a speed of 0.90m/sand a pressure of 170kPa.

(a) If the pipe tapers to 1.2cmand rises to the second floor 7.6mabove the input point, what is the speed and

(b) If the pipe tapers to 1.2cmand rises to the second floor 7.6mabove the input point, what is the water pressure at the second floor?

Short Answer

Expert verified

Hence, the pressure of water on the second floor is

Step by step solution

01

Given data

  1. The speed of the water at the basement level,.

  2. The diameter of the pipe at the basement level,.

  3. The pressure at the basement level,.

  4. The diameter of the pipe at the second floor,.

  5. The height of the second floor,.

02

Determining the concept

Determine the speed of the water at the second floor using the equation of continuity. Then, using Bernoulli’s equation, find the pressure of water on the second floor. According to Bernoulli’s equation, as the speed of a moving fluid increases, the pressure within the fluid decreases.

Formulae are as follows:

pu12ÒÏgg2h+constant

Av=constant

Where, pis pressure, vis velocity, his height, gis the acceleration due to gravity, his height, Ais the area, and ÒÏis density.

03

(a) Determining the speed of the water at the second floor

The water flow through the pipe obeys the equation of continuity,

Hence,

Hence, the speed of the water at the second floor is.

04

(b) Determining the pressure of water on the second floor

The water flow obeys Bernoulli’s principle as well,

Considering,, the density of water,,

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