Fluid product dispenser

A method of mounting a dispenser, the fluid dispenser comprising:

• a fluid reservoir including a neck that defines an opening;
• a dispenser member that is mounted in the opening of the neck, said dispenser member being suitable for delivering a quantity of fluid contained in said fluid reservoir, the dispenser member being provided with a dip tube that extends into the fluid reservoir so as to convey the fluid contained in the fluid reservoir to the dispenser member as a result of the dispenser member being actuated;
• and
• a cover tube that surrounds said dip tube at least in part, the cover tube including a free bottom end and a connection top end that is secured to a support element;
• wherein, in proximity of the connection top end, said cover tube includes at least one vent having a total flow cross sectional area that presents a size that is sufficient to enable the fluid to rise in the cover tube while the cover tube is being inserted into the fluid reservoir in the filled state, so as to reduce a displacement of fluid outside of the cover tube of the fluid in the reservoir as compared to a displacement of fluid outside of the cover tube from a comparative cover tube identical to said cover tube but lacking said at least one vent, the reduction in displacement of the fluid being a result of the air that is evacuated from the cover tube through said at least one vent as the cover tube is inserted into the fluid reservoir;
• and
• wherein the method comprises the following steps:
• the reservoir is initially filled with fluid up to the proximity of the neck;
• and
• the cover tube is immersed into the fluid of the reservoir through the neck, the fluid rising in the cover tube while the air initially present in the cover tube escapes through the vent, such that the top level of the fluid inside the cover tube always remains substantially the same as outside the cover tube.