So, to make a safe calculation, calculate the volume of wood you will be using, convert that to U.S. gallons, multiply that number by 8.33 pounds per gallon... and you will have the weight it wood take to sink the structure (see what I did there? lol) This number will be more than you strictly need since wood has some weight to it already, BUT I would double the sinker weight number to make sure it sinks and stays put. OR, at least multiply it by 1.5.

If wood weighed 8.33 pound per gallon (in other words, 62 pounds per cubic foot) the wood would not necessary float or sink..it would just hoover around with the current. Once you find something that weighs more than water (8.33 pounds per gallon)...it will sink.

There are more scientific weighs to calculate the OP's question (see what I did there? lol), but the above will get you where you need to be without making your head and my head hurt.

RossC is on the right track, just not in his right mind. Just kidding around Ross!

A true 2"x4"- 8 foot long makes up about 3.5 US gallons of volume. That would be 29 pounds of water weight minus most of the actual weight of the 2x4x8'. An untreated white wood 2x4x8" weighs about 10 pounds. You'd need 29-10=19 pounds to make it not sink or float. 19*1.5= about 30 pounds. This wood make it sink well (I did it again).