Need help with this(dimensional analysis)

  • Thread starter allaputa
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In summary, the relationship between velocity 'v', pressure drop 'P' and density 'p' for a liquid with a nozzle is expressed as v=C[P/p] raised to the power of 1/2. In terms of the fundamental units of kg, meter, and second, this equation can be written as v=C[(kg/meter*second^2)/(kg/meter^3)] raised to the power of 1/2.
  • #1
allaputa
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It is observed that the velocity 'v' of a liquid having a nozzle depends upon the pressure drop 'P'and the density'p'.Show that the relationship between them is of the form.


v=C[P/p]raised to power of 1/2
 
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  • #2
allaputa said:
It is observed that the velocity 'v' of a liquid having a nozzle depends upon the pressure drop 'P'and the density'p'.Show that the relationship between them is of the form.


v=C[P/p]raised to power of 1/2

What are your thoughts? What do you know?

Write v, P and [itex] \rho [/itex] in terms of the three fundamental units: kg, meter and second. Then the answer should be obvious.

Patrick
 
  • #3
I don't think anyone is going to miss the equation...:wink:
 

What is dimensional analysis?

Dimensional analysis is a mathematical method used to convert units and solve problems involving different units of measurement.

Why is dimensional analysis important?

Dimensional analysis is important because it helps ensure that calculations and measurements are accurate and consistent. It also allows for easy conversion between different units, making it useful in many scientific and engineering applications.

How do you perform dimensional analysis?

To perform dimensional analysis, you must first identify the units involved in the problem and their relationships. Then, use conversion factors to cancel out unwanted units and arrive at the desired unit of measurement.

What are some common mistakes when using dimensional analysis?

Some common mistakes when using dimensional analysis include forgetting to include conversion factors, using incorrect conversion factors, and not paying attention to units when writing out equations.

Can dimensional analysis be used for complex calculations?

Yes, dimensional analysis can be used for complex calculations involving multiple units and conversion factors. However, it is important to carefully track units and ensure that they cancel out correctly to arrive at the desired unit of measurement.

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