# Applications of Bernoulli’s Equation

Personalized homework help for all major subjects.

Order confidently with our risk free, 14-day money-back guarantee.

• ✔️ No sign-up required
• | 🔒 100% Confidential

## Our Expert Writers

We proudly boast a team of expert professionals with verified academic credentials, selected for their proven skills and flexibility through a strict process.

Engage with experts from the top universities across the globe.

## Get Homework Help Instantly

Say goodbye to homework stress! 📚 Just share your details and we’ll whip up an affordable quote in no time – often within 15 minutes.

Bernoulli’s equation is used to find out the measurement of various fluids’ (liquid and air) flowing rate with the assistance of certain flow rate measuring devices. Because of this aid, application of this equation is utilized in many fields.

3 of the most important measurement devices used for a fluid’s flow rate measurement are described here.

1. Pitot tube

For the measurement of the flow rate of a flowing fluid moving with a certain velocity, this device (Pitot tube) is used. This device has an ‘L’ shaped structure whose one end is open and is positioned above the fluid in the air. You will find the other side of the pitot tube kept immersed in that fluid. The positioning of the other side of the tube is about middepth point of it. This is done to measure the accurate velocity of that liquid or fluid.

To understand the working of this device in a better way, we will go through these following equations.

For that, we have to assume 2 points inside the flowing liquid before the application of Bernoulli’s equation. As stated, one point will be in the liquid, and the other will be at the mouth of the submerged sectionof the Pitot tube.

From that, we will get the equation,

P1 / p g + 1v2 / 2 g + z1 = p2 /p g + 2v2 / 2 g + z2

Now, at the beginning pointof the mouth of the tube inside the liquid, thekinetic head is converted so that it becomes pressure head.

So after conversion, its equation stands to be,

P1 /p g + 1v2 / 2g = p2 / p g

This equation can also be shown as,

H + v12/ 2 g = H + h

According to this equation, v1 = 2 g h

Here the action of ‘v’ is C v v1= cv 2gh

In this case, ‘cv’ is the coefficient of velocity for Pitot tube

Now, Oact in equational term will be,

Q act = Cv a 2 g h

Where, ‘a’ means cross sectional area of that Pitot tube.

Venturimeter

This device is also utilized for measuring the rate of flow of any fluid that flows through a pipe. Its unit is m3/s. Venturimeter is made up of 3 parts.

• The initial is a short converging part
• The second part is called throat, and
• The third is known as diverging part

With the help of a diagram depicting the Venturimeter, we will apply Bernoulli’s equation to 2 portions of this device. The first is in the inlet section of the pipe, and the second portion is the divergent part. Throat becomes the barrier that divides both the portions.

On application of this Bernoulli’s equation in both sections we will get,

P1 / p g + v1 / 2 g + z1 = p2 / p g + v2 / 2 g + z2

Suppose, this Venturimeter is kept is a horizontal position.

Because of this positioning, z1 = z2

So the equation for this horizontal position will be,

P1 / p g + v1 /2 g = p2 p g + v2 2 g

P1 –p2 / p g = v2 / p g + v2 / 2g

h = v2 – v2 / 2 g

Now from continuity equation,

a1 v1 = a2 v2

v2 = a1 / a2 v1 (equation 5.4)

Taking the value of v2 from the above equation we will get,

= (1a2 – 2a2 / 2a2) 1v2 / 2 g

1V2 = 2a2 / 1a22 a2

Its discharge value is calculated as,

Q th = a1 v1

Q th = a1 v2 / 1a2

= 2a2

= 2 g h

It is through the equation of this expression that you can find out the value of theoretical discharge.

This value is of theoretical discharge because in case of actual discharge there will be some type of losses.

This loss is represented by,

Q act = Cd x Q th

where, Cd is known as the coefficient of discharge for a Venturimeter.In this case, the value of Cd is less than 1.

Now, in case of using a different manometer, expression for this device’s horizontal positioning is,

h = x [S h / So – 1]

In this different manometer, certain values describe the workings and equation of this Venturimeter.

S h = special gravity of heavier liquid

x = difference of heavier liquid inside the u-tube

S0 = special gravity of liquid flowing through pipe of Venturimeter

In this case, S0is greater than S h.

Now, in a certain instance if S h is greater than S0, then expression of ‘h’ will change, and its new expression will be,

h = x [1 – St / So]

Here,

x = difference of lighter liquid inside the u-tube.

S1 = special gravity of the lighter liquid

If this Venturimeter is inclined to a certain position, then,

z1 = z2

h = (p1 / p g + z1) – (p2 / p g + z2)

= x [S h / So – 1]

Orit can also be stated as,

[1 – St / So] x

Orifice Plate or Orifice meter

In case you need to measure the rate of flow of a fluid which flows with restriction or with a reduced pressure, an orifice plate or orifice meter is an apt device. With it, you can determine its mass flow rate or volumetric rate.

For an effective measurement, a circular sharp edge plate is generally utilized in this device.

Before we apply Bernoulli’s equationto this device, we will divide it into 2 sections.

1. Minimum cross section at vena contracta, which is the half circular lower section of this device
2. Upper half of this device from where the fluid flows. It is basically that section where the orifice plate is positioned.

After the application of Bernoulli’s equation in both the sections, the equation stands at,

P1 / p g + 1v2 / 2 g + z1 = p2 / p g + 2v2 / 2 g + z2

On simplifying this equation,

(p1 / pg + z1) – (p2 / p g + z2) = 2v2 /2 g – 1v2 / 2g

Now,

h = 2v2 / 2 g – 1v2 / 2 g

a2 v2 = a1 v1

v2 = a1 / Cc a o v1

Here C represents coefficient of contraction

From the above, the new equation will be,

h = (a12/(Cc2 .  a02)-1)  v12/(2 g) = ((a12-Cc2-Cc2a02)/(Cc2 .  a02))  v12/(2 g)

v12 = ((Cc2 .  a02)/(a12- Cc2 .  a02))2 gh

v1 = ((Cc .  a0)/√(a12- Cc2 .  a02)) √(2 g h)

Q = a1v1

= a1 x ((Cc .  a0)/√(a12- Cc2 .  a02)) √(2 g h)

Q = ((a1 .  Cc .  a0)/√(a12- Cc2 .  a02)) √(2 g h)

On simplifying the entire equation with the help of the relation between Cd and C, we will get the following equation.

√(a12 – Cc .  a02) =  Cc/Cd √(a12-a02)

So, Q = (Cd .  a0 .  a1  √(2 g h))/√(a12-a02)

Here, Cd (orifice) is way less than Cd (Venturimeter).

It is represented as Cdorifice<< Cd Venturimeter.

Cd is the coefficient of discharge for this device (orificemeter).

Links of Next Mechanical Engineering Topics:-

Pricing may change based on requirements

l

## FAQ - Frequently Asked Questions

Discover quick answers in our FAQ, covering the most common customer questions about our homework help service.

### Is your homework service confidential?

M
L

Absolutely! Confidentiality is one of the basic guarantees of our service at MyHomeworkHelp.com.

When our customers make their homework orders, they know their information remains 100% confidential.

Even your homework writer will not be provided with your personal details. So, when you hire a professional homework helper on our website, rest assured that your information will remain private and safe.

### Who will help me with my homework?

M
L

We work with subject experts from all over the world. We hire them with the help of complex tests in the disciplines of their expertise. We also verify the IDs and academic transcripts of our homework writers to be sure that our experts have a bachelor's or master’s or a PhD degree. This is how we can be sure of the proficiency of our panel of experts who will help you with your homework.

### Is it legal to ask for help with homework?

M
L

Seeking homework help is perfectly fine and shows your proactive approach to overcoming challenges. But it's important to use our homework service to enhance your understanding, not to replace your own efforts.

Our homework service offers original solutions for personal use, including:

• Generating ideas or arguments for your research.
• Direct citation, with proper referencing.

However, it's crucial to avoid plagiarism by not submitting our work as your own. Make sure to check your institution's academic integrity policies before using our services. Our goal is to support your educational journey in a responsible and beneficial way. Refer our honor code for more details.

### Is myhomeworkhelp.com legit?

M
L

Yes, myhomeworkhelp.com is completely legitimate. We've been successfully connecting students with top experts worldwide since 2012, offering direct, secure communication for a seamless learning experience. With over thousands of students helped and a commitment to innovative, effective education tools, we're dedicated to making learning easier and more accessible for everyone.

You can read our reviews here on Trustpilot and Sitejabber (Independent, verified reviews from buying customers) like you!

### Is there a possibility of plagiarism in my completed order?

M
L

Unlike our competitors who use cheap and ineffective in -house plagiarism software, MyHomeworkHelp.com uses credible software to check your homework solution originality. We guarantee that your paper will pass TurnItIn checks with a low percentage of similarity. In addition, we also check submitted papers for ai-content using Originality.ai.

You will receive a complemantary plagiarism free report with your completed order.

### What makes you one of the best homework help website?

M
L

We are not number 1 (yet!). We're an independent, bootstrapped business standing up to Big EdTech for last 12 years. So it means a lot that folks like you are willing to consider our services for your educational needs.

Myhomework Help is recognized as one of the premier websites for homework answers for three key reasons.

1. Firstly, we pride ourselves on the expertise and qualifications of our tutors/experts, who are selected through a rigorous vetting process to ensure they can provide best academic assistance across a wide range of subjects.
2. Secondly, our response time to student inquiries is fast (as early as few minutes), reflecting our understanding of the importance of timely support in an academic setting.
3. Lastly, we keep our pricing very student friendly. Our aim is to provide the best learning experience to students like yourself without burning a hole in your pockets.