Today I puzzle over a dimensionless rate of sink, and a new cover set for an old iPad arrives, but not without problems.

## Dimensionless rate of sink

Today I’ve been trying to resolve an issue in regards to dimensionless rate of sink. It’s supposed to be in relation to the current rate of sink and the minimum rate of sink:

$\widehat{R}_S=R_S/R_{S,min}$

but the formulas that I had entered late at night involving velocity for minimum sink, resulted in different results.

$\widehat{V}=V/V_{minS} \\ \widehat{R}_S=\frac{\widehat{V}^4+3}{4\widehat{V}} \\ \widehat{R}_S=\frac{\widehat{V}^3}{4}+\frac{3}{4\widehat{V}}$

As shown above they are correct, but the mistaken way that they were entered resulted in three formulas that all produced different results.

// bad versions of formula
var rshat = rs / rsmin; // 1.113
...
var rshat = (Math.pow(vhat, 4) + 3) / 4 * vhat; // 0.659
...
var rshat = Math.pow(vhat, 3) / 4 + 3 / 4 * vhat; // 0.613


This occurred due to a lack of parenthesis around the lower part of the fraction, which resulted in the following mistaken formula instead

$\widehat{R}_S=\frac{\widehat{V}^3}{4}+\frac{3}{4}\widehat{V}\text{ (incorrect version)}$

Once I understood the problem and corrected that, everything now works as it should do.

// correct versions of formula
var rshat = rs / rsmin; // 1.113
...
var rshat = (Math.pow(vhat, 4) + 3) / (4 * vhat); // 1.113
...
var rshat = Math.pow(vhat, 3) / 4 + 3 / (4 * vhat); // 1.113


## New cover for an old iPad

The cover + protector + pen for an old iPad that was ordered last month from aliexpress has at last arrived. I made the foolish mistake though of signing for it before checking that everything was okay. The cover has a small split in the back, which is mostly cosmetic but is still a problem. Now that I’ve signed for it though I can’t do much to address the problem. My only option now is to post it back for a refund, but the cost of postage from here is more than the refund is worth.

So consider this a lesson learned – always check the items in the parcel before signing off on them.