# Calculating Volumetric Flow Rate: A Complete Guide

## How do we find the volumetric flow rate given the data below?

Water at 20°C discharges from a storage tank through a 150 m length of horizontal pipe. The pipe is smooth and has a diameter of 75 mm. The entrance to the pipe is square edged with a loss coefficient of 0.5. The depth of water needed to produce a volumetric flow rate of 0.1 m³/s is about:

1. Calculate the velocity of the flow.

2. Determine the Reynolds number and find the friction factor.

3. Calculate the head loss due to friction and the head loss due to the coefficient of 0.5.

4. Find the total head loss.

## Solution:

To find the volumetric flow rate, we need to follow these steps:

1. Calculate the velocity of the flow:

Given diameter of the pipe (D) = 75 mm = 0.075 m

Given volumetric flow rate = 0.1 m³/s

Using the formula Volume flow = area x velocity, we get:

0.1 m³/s = π(0.075/2)² x velocity

Therefore, velocity = 2.83 m/s

2. Determine the Reynolds number and find the friction factor:

Calculate Reynolds number (RE):

RE = ρVD/μ = 998 x 2.83 x 0.075 / 1.002 x 10⁻³ pa.s = 2.11 x 10⁵

Calculate friction factor (f):

f = 0.079 / (2.11 x 10⁵)^1/4 = 0.00267

3. Calculate the head loss due to friction and the head loss due to the coefficient of 0.5:

Head loss due to friction (hl):

hl = (4 x 0.0195 x 150 / 0.075) x (2.83²) / (2 x 9.81) = 63.68

Head loss due to coefficient of 0.5 (hlc):

hlc = 0.5 x (2.83²) / 2 x 9.81 = 0.204

4. Find the total head loss:

Total head loss = 63.68 + 0.204 = 63.88 meters

Calculating the volumetric flow rate involves several key steps, including determining the velocity, Reynolds number, friction factor, and head loss. By following these calculations, we can accurately find the volumetric flow rate of a fluid through a pipe.

Understanding the principles behind these calculations is crucial for engineers and professionals working in fluid mechanics. By mastering these concepts, one can effectively analyze and design piping systems to ensure optimal flow rates and efficiency.

Practice more exercises on volumetric flow rate to enhance your skills and knowledge in fluid mechanics.