Calculation of Flow rate

In summary, flow rate is the volume of fluid that passes through a given point in a specific amount of time. It is an important measurement in various fields such as plumbing, chemical reactions, and environmental studies. Flow rate is calculated by dividing the volume of fluid passed by the time it took to pass through a given point. Several factors can affect flow rate, including the type of fluid, viscosity, pipe diameter, and pressure. It can be measured using different devices and techniques depending on the application. Some common units used to express flow rate include liters per second, cubic meters per hour, gallons per minute, and cubic feet per minute.
  • #1
penpepper
2
0
suppose there is an spherical balloon say 100 cu.m . The pressure difference between the air in it and surrounding air is 200N/m2 . If a hole of 1 sq.m is made what will be the flow rate from it. Of course the flow rate will decrease as the time progresses but how to determine it over a period of time??
 
Engineering news on Phys.org
  • #2
Is this a homework problem? What equations apply?

1 m2 is a BIG hole!

200 Pa is a very small differential pressure. 1 atm = 101325 Pa = 101.325 kPa = 0.101325 MPa or thereabouts.
 
  • #3


To calculate the flow rate from the hole in the spherical balloon, we can use the Bernoulli's equation, which states that the total pressure in a fluid system remains constant. In this case, we can assume that the pressure inside the balloon is equal to the atmospheric pressure outside.

Using the given information, we can calculate the initial flow rate using the equation:

Q = A√(2ΔP/ρ)

Where Q is the flow rate, A is the area of the hole, ΔP is the pressure difference, and ρ is the density of the fluid (in this case, air).

Plugging in the values, we get:

Q = 1 sq.m * √(2 * 200N/m2 / 1.2 kg/m3)

Q = 1 sq.m * 10.825 m/s

Q = 10.825 m3/s

This means that initially, the flow rate from the hole in the balloon will be 10.825 cubic meters per second.

To determine the flow rate over a period of time, we need to take into account the decrease in pressure inside the balloon as the air flows out. This can be calculated using the ideal gas law:

P1V1 = P2V2

Where P1 and V1 are the initial pressure and volume inside the balloon, and P2 and V2 are the final pressure and volume after a certain amount of air has escaped.

We can rearrange the equation to solve for V2:

V2 = (P1V1)/P2

Using the given values, we can calculate the volume of air that has escaped after a certain amount of time. For example, if after 1 minute, the pressure inside the balloon has decreased to 150N/m2, the new volume can be calculated as:

V2 = (200N/m2 * 100 cu.m) / 150N/m2

V2 = 133.33 cu.m

This means that after 1 minute, 100-133.33 = 33.33 cu.m of air has escaped from the balloon. We can then use this new volume to recalculate the flow rate using the same equation as before.

As time progresses, the pressure inside the balloon will continue to decrease and the flow rate will decrease accordingly. To accurately determine the flow rate over a longer period of time, we would need to continuously recalculate the volume of air that has
 

What is flow rate and why is it important?

Flow rate is the volume of fluid that passes through a given point in a specific amount of time. It is an important measurement in many fields of science and engineering, as it helps determine the efficiency, capacity, and performance of systems and processes involving fluids. For example, in plumbing, flow rate is crucial in ensuring proper water supply and drainage. In chemical reactions, flow rate helps control the rate of reaction and the distribution of reactants. In environmental studies, flow rate is used to monitor water and air pollution levels.

How is flow rate calculated?

Flow rate is calculated by dividing the volume of fluid passed by the time it took to pass through a given point. The formula for flow rate is: flow rate = volume / time. The volume can be measured in different units such as liters, gallons, or cubic meters, while time is usually measured in seconds, minutes, or hours. The resulting flow rate can be expressed in different units, depending on the application, such as liters per second, cubic meters per hour, or gallons per minute.

What factors can affect flow rate?

Several factors can affect flow rate, including the type of fluid, the viscosity of the fluid, the diameter and length of the pipe or channel, and the pressure or force applied to the fluid. For example, a thicker or more viscous fluid will have a lower flow rate than a thinner or less viscous fluid. Similarly, a smaller diameter pipe will have a lower flow rate than a larger diameter pipe, given the same pressure and fluid properties. Changes in temperature and altitude can also affect flow rate.

How can flow rate be measured in real-life situations?

Flow rate can be measured using various devices and techniques, depending on the specific application. In plumbing, flow rate can be measured using a flow meter or by simply timing how long it takes to fill a container with water. In chemical reactions, flow rate can be monitored using sensors and data loggers. In environmental studies, flow rate can be measured using specialized equipment such as stream gauges, pitot tubes, or velocity meters.

What are some common units used to express flow rate?

Some common units used to express flow rate include liters per second, cubic meters per hour, gallons per minute, and cubic feet per minute. In scientific and engineering applications, flow rate may also be expressed in terms of the mass of fluid passing through a point per unit time, such as kilograms per second or pounds per hour. Additionally, flow rate may be expressed in terms of velocity, such as meters per second or feet per minute, which can be converted to flow rate by multiplying with the cross-sectional area of the pipe or channel.

Similar threads

Replies
3
Views
229
  • Mechanical Engineering
Replies
4
Views
759
  • Mechanical Engineering
Replies
20
Views
607
  • Mechanical Engineering
Replies
15
Views
1K
Replies
6
Views
2K
  • Mechanical Engineering
Replies
4
Views
1K
  • Mechanical Engineering
Replies
8
Views
1K
Replies
5
Views
4K
  • Mechanical Engineering
Replies
5
Views
12K
  • Mechanical Engineering
Replies
0
Views
311
Back
Top