Download Prospectus


How can continuity affect engineering problems?

In our previous article, we looked at how heat and temperature can affect engineering problems.  In this article, we’re going to look into continuity and how it affects engineering problems.

What is continuity?

If we consider a steady flow at velocity, v, of a fluid with a density of p.  This flow is through a pipe with varying cross-section, A, that you can see in the image below: 

, How can continuity affect engineering problems?

The equation of continuity states that the rate of mass entering the pipe has to be equal to the rate of mass leaving the pipe.  This is a state of the principle of conservation of mass. 

The mass flow rate,, is defined as:

, How can continuity affect engineering problems?

 Therefore, if we consider the two stations 1 and 2 that are shown in the image above, we can say that:

, How can continuity affect engineering problems?

Incompressible Continuity Equation

We can define the Mach number, M, using this equation:

, How can continuity affect engineering problems?

Here, v represents the mean local flow velocity, measured in m/s.  Also, a represents the local speed of sound.  The speed of a sound is a function of the fluid and temperature.  If we have v = a and M = 1, then this represents a flow speed that is equal to the speed of sound.

If we have a relatively low-speed flow, of M as less than 0.3, then it can be assumed to be incompressible.  This means that the density can be considered to be constant.  Therefore, we can state that a simplified version of the continuity equation for incompressible flow would be:

, How can continuity affect engineering problems?

And therefore:

, How can continuity affect engineering problems?

Real-life examples

Let’s have a look at some real life examples to see how this works.  If we take the convergent duct that’s in the image below, we can calculate the flow speed at the exit, which is point 2.

Our continuity expression, as we’ve seen above, is:

, How can continuity affect engineering problems?

Now, if we rearrange if with respect to the unknown parameter, we will get:

, How can continuity affect engineering problems?

Now, we can substitute the values we have, and solve the equation:

, How can continuity affect engineering problems?

We can do a sanity check on our equation to make sure it’s right.  The area of the duct has reduced going from station 1 to station 2, or from the entrance to exit.  Going by continuity, and to be able to maintain the constant value of mass flow there has to be a corresponding increase in velocity.  The flow speed has increased, and we can see this from our solution.  This gives us an additional sanity check to ensure our answer is correct.

We can use the same equation to solve an incompressible fluid flowing through a pipe with a diameter of 20mm.  The velocity of the fluid is 10m/s.  If the pipe changes diameter to 25mm, we can calculate the velocity at the point that it changes.  Our answer would be 6.4m/s, and we can use a similar sanity check to ensure our answer is correct.

Keep an eye out for our next article looking into how ideal gas laws can affect engineering problems.

Interested in our courses?

You can read more about our selection of accredited online mechanical, electrical, civil and aerospace engineering courses here.

Check out individual courses pages below:

Diploma in Material Science

Diploma in Aircraft Design

Diploma in Aerospace Structures

Diploma in Principles of Flight

Diploma in Aerodynamics, Propulsion and Space

Higher International Diploma in Mechanical Engineering

Higher International Certificate in Mechanical Engineering

Diploma in Mechanical Engineering

Diploma in Mechanical Technology

Alternatively, you can view all our online engineering courses here.

Recent Posts

How can we select engineering materials?

How can we select engineering materials? In our previous article, we looked at elastic and magnetic hysteresis. In this article, we’re going to look at how we can select engineering materials.  In other articles, we have previously looked at the different materials and their properties.  However, it’s important that engineers understand how we can go […]

What is hysteresis?

What is hysteresis? In our previous article, we looked at the material modes of failure we need to be aware of in engineering. In this article we’re going to dive into elastic and magnetic hysteresis. Elastic Hysteresis Elastic hysteresis is the difference in strain of a material during loading of stress or strain, versus during […]

What are material modes of failure?

What are material modes of failure? In our previous article we looked at the properties of engineering materials. In this article,  we’re going to dive into material modes of failure and what they are. What is failure? The definition of failure is that the component is no longer fit for use or its designed purpose.  […]