No

"Head" as you have termed it is a measure of pressure and will therefore be independent of the volume. Remember using a U-tube manometer in the school physics lessons?  If you raise the level of the reservoir by a foot, the water travels a foot up the tube, regardless of the diameter of the tube (and provided your reservoir holds sufficient water).

Andy Machon

 
 

Afoot of head is about .4333333333333pounds per square inch

Adding to the above...

I think the thing that you failed to see was the difference between PRESSURE and FORCE.  A big column will have a bigger FORCE at the bottom, but it is also distributed over a bigger area.  Hence, the pressure will be the same no matter what the diameter is--for the same fluid, anyway.

The term 'head' is used to indicate the pressure exerted by the fluid. Pressure by definition is the force per unit area. The force exerted by the column of liquid say, water is the weight of the liquid column, which is given by

Area of cross section  x  height of the liquid column  x  specific weight of the liquid.

Therefore pressure is given by

Force/area = height of the liquid column  x  specific weight of the liquid.

Since, the specific weight of the liquid is a constant (of course at a given temperature), the pressure is expressed as so many'feet' of the liquid column. Hence, It is also important that the 'head' should always be associated with the fluid of reference, such as, 10 m. of water or 76 cm. of mercury etc. The pressure is obtained by multiplying the head by the specific weight of the fluid.

Trilinga