If the pressure of water at one point in a pipeline is 117.3 kPa and reduces to 110 kPa with a head loss of 0.2, what is the velocity at the second point?

To determine the velocity of water at the second point in the pipeline, it is essential to use the principles of fluid dynamics, specifically Bernoulli's equation, which relates the pressure, density, velocity, and height of a fluid in steady flow.

First, we recognize that a change in pressure leads to a change in the velocity of the fluid. Given the initial pressure is 117.3 kPa and the final pressure is 110 kPa, we can calculate the drop in pressure:

[

\Delta P = P1 - P2 = 117.3, \text{kPa} - 110, \text{kPa} = 7.3, \text{kPa}

]

Next, it's important to convert these pressures into units compatible with the velocity equation. The density of water is approximately (1000 , \text{kg/m}^3), and we convert the pressure drop into pascals:

[

7.3, \text{kPa} = 7300, \text{Pa}

]

Bernoulli's equation states that the pressure drop in a flowing fluid can be related to its velocity through the following rearrangement:

[

\Delta P = \frac{1