# Fluid dynamics continuity equation

• Nanu Nana
In summary, the conversation discusses the necessary velocity of air flow through a cylindrical heating tube in order to heat a rectangular space of specific dimensions. The equation for flow rate is mentioned, as well as the continuity equation, and the use of the area of a cylinder to determine the necessary radius of the tube. The correct equation for the area of a circle is also mentioned.
Nanu Nana

## Homework Statement

Through a (cylindrical) heating tube, warm air has to flow with a velocity of 3m/s in order to heat a rectangular spacewhich is 12 m long, 10 m wide and 2.5 m high. How large the radius of the tube should be if the air in the room get refreshed every 15 minutes ? Assume that the air-density in the tube and in the room are equal.

## Homework Equations

Continuity equation
A1 x v1 = A2 x v2[/B]

## The Attempt at a Solution

Flowrate = Volume/ t V/t = A x v
Flowrate = 12x10x2.5 = 300 m3 / 900 s = 0.33
0.33 = A2 x 3m/s
A2= 0.111 m^2
So to find the radius you have to use area of cilinder
A=pi x 2x (r)^2
0.111= pi x 2x (r)^2
r= 0.132 m why do i get this answer ?? . Its wrong .answer has to be 0.1881 [/B]

What is the equation for the area of a circle?

A= pi x (r)^2
Now its correct
Thank you

## 1. What is the continuity equation in fluid dynamics?

The continuity equation is a fundamental principle in fluid dynamics that states that the mass of a fluid entering a given region must equal the mass leaving that region, assuming there is no accumulation or depletion of fluid within the region.

## 2. How is the continuity equation derived?

The continuity equation is derived from the conservation of mass principle, where the total mass of a system remains constant over time. It is also based on the concept of conservation of flow rate, which states that the volume of fluid flowing through a given area must remain constant.

## 3. What are the applications of the continuity equation?

The continuity equation has a wide range of applications in fluid dynamics, including analyzing the flow of liquids and gases in pipes, pumps, and turbines, as well as studying the behavior of fluids in open channels and rivers. It is also used in meteorology, oceanography, and aerodynamics.

## 4. What are the assumptions made in the continuity equation?

The continuity equation assumes that the fluid is incompressible, meaning its density remains constant. It also assumes that the fluid is flowing steadily and that there are no external forces acting on the fluid, such as gravity or friction.

## 5. How is the continuity equation used in practical applications?

The continuity equation is used in practical applications to analyze and predict the behavior of fluids in various systems. It allows engineers to design and optimize systems such as pipelines, pumps, and turbines for efficient and safe operation. It is also used in weather forecasting and water resource management.

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