Question

A water pipe having a $2.5cm$inside diameter carries water into the basement of a house at a speed of $0.90m/s$and a pressure of $170kPa$.

(a) If the pipe tapers to $1.2cm$and rises to the second floor $7.6m$above the input point, what is the speed and

(b) If the pipe tapers to $1.2cm$and rises to the second floor $7.6m$above the input point, what is the water pressure at the second floor?

Short answer

Hence, the pressure of water on the second floor is

Step-by-step solution

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,.

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:

$pu\frac{1}{2}\rho g{g}^{2}h+$constant

$Av=$constant

Where, $p$is pressure, $v$is velocity, $h$is height, $g$is the acceleration due to gravity, $h$is height, $A$is the area, and $\rho$is density.

(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.

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

The water flow obeys Bernoulli’s principle as well,

Considering,, the density of water,,