There is no point reaching for a calculator that cannot show its working. This one starts from inner radius of the tube (a), gravitational acceleration (g), height of the liquid in the tube (h), pressure inside (pᵢ), pressure outside (pₒ), density of the liquid (ρ), surface tension, contact angle (θ) and cos and reports radius of the meniscus (r) and pressure difference (δp), so you can see how each answer follows from the numbers you entered.
What Is the Young Laplace Equation Calculator?
The young laplace equation calculator turns inner radius of the tube (a), gravitational acceleration (g), height of the liquid in the tube (h), pressure inside (pᵢ), pressure outside (pₒ), density of the liquid (ρ), surface tension, contact angle (θ) and cos into radius of the meniscus (r) and pressure difference (δp).
It is a quick way to get from the numbers you have to the number you need, without setting up a spreadsheet or reaching for a formula.
How the Young Laplace Equation Works
Each result follows from the ones before it, and the calculator shows every step, so a surprising answer can be traced back to the input that caused it.
Round your inputs to the precision you actually know, and keep more precision than that in the intermediate steps.
Getting a Result You Can Trust
Run the calculation twice with slightly different inputs. A sensible calculator moves its output in proportion; a wild change points to a unit or a decimal point problem in what you entered.
Write the inputs down next to the answer. It takes a moment and it is the difference between a number you can explain and one you cannot.
A Worked Example
Working through an example, with inner radius of the tube (a) set to 10, gravitational acceleration (g) set to 5, height of the liquid in the tube (h) set to 2, the calculator returns pressure difference (δp) of -90, and radius of the meniscus (r) of 11.59664. Substitute your own figures and the same steps produce the same kind of answer.
Frequently Asked Questions
What do I need to work out radius of the meniscus (r)?
Enter inner radius of the tube (a), gravitational acceleration (g), height of the liquid in the tube (h), pressure inside (pᵢ), pressure outside (pₒ), density of the liquid (ρ), surface tension, contact angle (θ) and cos. The calculator then works through the relationship and reports radius of the meniscus (r) and pressure difference (δp).
What does the young laplace equation actually calculate?
It takes inner radius of the tube (a), gravitational acceleration (g), height of the liquid in the tube (h), pressure inside (pᵢ), pressure outside (pₒ), density of the liquid (ρ), surface tension, contact angle (θ) and cos and converts them into radius of the meniscus (r) and pressure difference (δp) using the standard relationship for this problem. Each step is applied in turn, so every output is traceable back to the numbers you typed in.
How should I enter inner radius of the tube (a)?
Use the value you actually have, in the unit shown next to the field. Enter every value in the same unit system. The calculator assumes the figures you supply are consistent, so it cannot correct a mistake that happens before the calculation starts.
Can I use this for a quick estimate as well as a precise answer?
Yes. The calculator is built for quick checks, so round your inputs to a sensible number of significant figures and the result will be just as useful. If you need more precision, keep the same method and add digits to the inputs rather than adjusting the method itself.
Do I have to fill in every field?
Only the fields a particular result depends on. If you leave one blank, the results that need it simply show a note instead of a number, and everything else still works.