Method for determining the size of a leak

A method for determining the cross sectional area of a leak in the liquid-containing tank device of a vehicle, in particular of a motor vehicle, the liquid influencing the pressure in the tank device by evaporation, with the following steps:

• generating a first pressure as a reference pressure in the tank device at a first instant (t1),
• detecting a first pressure characteristic up to a second instant (t2),
• generating a second pressure at a third instant (t4), the first pressure and the second pressure being chosen to be different,
• detecting a second pressure characteristic up to the fourth instant (t5),
• determining the pressure gradient of the first pressure characteristic at the second instant (t2) and of the pressure gradient of the second pressure characteristic at the third instant (t4),
• determining the first pressure difference of the pressure at the second instant (t2) from the reference pressure,
• determining the second pressure difference of the pressure at the third instant (t4) from the reference pressure,
• computing the cross sectional area of the leak depending on the determined pressure gradient and the pressure differences, based on an equation:
• A
• =
• ⁢
• (
• V
• p
• ⋆
• α
• ⋆
• ρ
• 2
• ⋆
• R
• ⋆
• T
• )
• ⋆
• 1
• Δ
• ⁢
• ⁢
• p
• 4
• ⋆
• {
• {
• (
• dp
• /
• dt
• )
• 4
• -
• (
• dp
• /
• dt
• )
• 2
• }
• (
• 1
• +
• Δ
• ⁢
• ⁢
• p
• 2
• Δ
• ⁢
• ⁢
• p
• 4
• )
• }
• ,
• wherein
• A is the cross sectional area of the leak,
• V is the volume of the tank device,
• p is the density of a gas flowing through the leak,
• α is a flow characteristic that designates the leak as an orifice plate,
• R is the universal gas constant,
• T is the temperature of the gas flowing through the leak,
• Δp2 is the first pressure difference,
• Δp4 is the second pressure difference,
• (dp/dt)2 is pressure gradient of the first pressure characteristic at the second instant, and
• (dp/dt)4 is the pressure gradient of the second pressure characteristic at the third instant,
• assuming that the evaporation rate is constant in the tank device, and that a leak rate is established which is proportional to the square root of the respective pressure difference.