I have a small 50 gallon pond. I'm getting an urge to dig out a stream,
maybe 15-20 foot in length, 18 inches wide, 6-12 inches deep....





My biggest concern is what I have quoted above.
Your say your pond is 50 gallons, which is about 220 litres

There will be more water in your stream than in your pond! When you switch
your pump on for the first time, you will find that your pond will be empty
before the first drop of water has gone all the way around the circuit in to
your pond again.

Even a stream 15ft x 12inches x 6 inches is about as much water than is in
your pond.

(I like to use metric for these calculations : 457cm x 30cm x 15cm =
206000ml = 206 litres = 46 gallons)

Dont forget that I did not allow for any water in the hose in my
calculations.

My suggestion is to opt for a significantly smaller stream, or get a bigger
pond.
A stream measuring 15ft long by 12 inches wide and only one inch deep is
still 7 gallons of water!
Even that will cause a level-drop of 14% in your pond when you switch the
pump on.

regards

Brendan