Filling of Tank

Too many variables, too little information.
Make the hole big enough and the flow coming out will be the same as the flow going in.
Del

Velocity will be constant at the point, when rate of change of water level due to inflow = rate of change of water level due to outflow, when it will happen? will depend on the construction of outlet hole, size of outlet hole and amount of friction at outlet, and may be few more factors, This is the point when outlet and inlet flow will equalise, You can also get a constant flow at outlet if tank start overflowing.

Mathematics? sorry!!

When outlet is submerged, the flow will behave as a submerged oriface.

When partially submerged, you have weir-flow.

When not submerged, you have no-flow.

Is the tank vented? Diameter? etc.?, etc.?

Mind if I use this. "When not submerged, you have no-flow" I think it"s very funny when thinking of holes.

If you can tell me the flow rate and the size of the hole, I can calculate the average velocity. I specify "average velocity" because the velocity at the center of the hole will be greater than the velocity near the edge.

i just want to know the approach to find this.so please take your own values for the variables.

To me it appears like a student homework, for which this forum is not meant.

Using control volume analysis and applying the law of conservation of mass I ended up with a differential equation (contains both a function of "h" (tank elevation above the hole) and its derivative). The bad news is that I don't think it is solvable (I'll keep investigating though), so I doubt you will find a function for the velocity.