I want to build a NAS with a single 2.5 ssd.
According to this video It should be possible. do I need a additional power supply for the hard drive?
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The key thing with any Pi especially the 3B+ or 4 models is to make sure you are using a proper power supply and not a generic (or even branded charger).
Power supplies (esp. the RPF/RPT ones) are designed to cope with power surges (such as hard drives spinning up), increased number of cores (e.g. start up of programs or extra processing requirements) or demands from GPIO connected devices / HATs.
The majority of charges can drop the voltage temporarily to cope with the surge in current requirements to say nothing of initial loss over the cables. The cheap charger cables can cause significant loss due to the thinness of them.
The older drives with two USB connectors where designed to be used across two USB hubs on laptops or PCs allowing the two chips driving the ports to provide power without exceeding the current limits of the chip (or connectors). Unfortunately, the majority of Pi boards only use one hub (despite a plethora of USB ports) so a dual USB cable may not help unless you can confirm the power draw is via two hubs.
So far, the only issue I have found with spinning hard disk drives have been the 4Tb ones - I've not been able to get them to reliably work without a powered hub - I normally get more issues from the USB / SATA interface not booting.
That last point is also worth noting - not all drives will allow the Pi computers to boot from them. Linux has spotty support for USB devices and earlier Pi boards would only boot from some adapters and not others (even though they looked the same). A work around for early boards was to use the SD card to hold the bootcode file and load the rest from the hard drive, with another to tell the OS to load from the drive by reconfiguring part of the OS to point to the hard drive.
With a single drive NAS, I would consider using the SD card to hold the operating system and configuration and keep the data on the hard drive only. This lets you simply copy the SD card to another machine as backup. For example, a copy of config.txt / fstab and Samba files from the SD card will get you a basic NAS up and running from backup in under 30 minutes assuming the hard drive data is not corrupt.
If you want to use an SSD as shown in the video you won't need an extra power suppply. However if you use an HDD you may need an extra power supply depending on what cabel you use to connect the HDD to your pi. Some cables for HDDs especially older ones come with two USB cables one for data and one for power. Since the Pi has 4 USB ports there should be no Problem setting this up.