what i include in my rentals:
* air pump - to quickly inflate the pool
* 2 hoses - one is a drinking water hose (so the hot water doesn't leach PVC/lead/etc. into the water welcoming your baby) to fill, a regular garden hose to empty
* a 9'x12' tarp - to protect the floor
* a small sieve or fish net - to scoop out the nasties
* pool thermometer - nice to have, not a must... as the PP said, you can just dip a regular thermometer into the water...
* a small bucket - for quickly bailing out the pool, if necessary (ie: partner gets into the pool with you and you need to take some water out)
* a sump pump
* lots of old towels
general tips:
* tap adaptor - make sure you have the right one for your faucet BEFORE you're in labour...
* hoses - make sure they're long enough to get from your water source to where you're setting up the pool BEFORE labour...
* water temperature - generally, you don't want the temperature hotter than 35-38 degrees celsius...
* remember that you may have to fill the pool in stages, depending on the size of the pool and your hot water tank... i usually suggest that people half-fill the pool with very hot water when they know labour is established, so you have less filling time when you want to get in... then just top up with hot/cold water to make it the right temperature when you're about to get in... just put a broom handle or something like that across the top of the pool and then cover it with a plastic sheet of some sort then a few quilts or comforter... that can keep the water hot for 6-12 hours...
* if you're not intending to re-sell then you can skip the liner... cleaning the pool with a 1:10 bleach to water solution is sufficient to kill any bodily fluids that may have been left on the pool from the previous owner before you use them (because liners often leak)...
* if you want the liner, buy the one that fits your pool... nothing is more frustrating that not having the pool liner slip off once the pool is filled...
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