One way to administer an inoculation is with a "gun" which shoots the vaccine via a narrow opening. No needle in required, for the vaccine emerges with sufficient speed to pass directly to the tissue below the skin. The speed is high, because the vaccine (1170 kg/m^3) is held in a reservoir where a high pressure pushes it out. The pressure on surface of the vaccine in one gun is around 4200000 Pa above the atmospheric pressure exterior the narrow opening. The dosage is small sufficient that the vaccine's surface in the reservoir is almost stationary throughout an inoculation. The vertical height between the vaccine's surface in the reservoir and the opening can be avoided. Determine the speed at which the vaccine emerges.