Trailb78:
The barrel length is measured from the muzzle to the forcing cone in front of the cylinder. You will probably find it is a 5 inch barrel.
The serial number you have given is taken from the underside of the barrel. The B Prefix indicated a barrel. Check the underside of the grip frame, you may have to take off the grips to see the actual serial number.
The gun has a long action, so it predates 1949.
If the serial number is 564169 then it it s .38 Military & Police Model of 1905 4th Change manufactured 1926 or 1927.
If the serial number is V564169 then it is a .39 Victory Model manufactured 1943 or 1944.
The grips appear to be early diamond targets from the 1950s, there may be some collectors value.
This particular gun predates the internal hammer block safety introduced in 1944. If dropped it could fire, so leave the chamber under the hammer empty.
Generally value is low on well worn examples, possibly $250. Because of the provenance and the grips you may find a collector willing to pay a bit more. I suggest you check at
www.smith-wessonforum.com if you are considering selling.