TSHong

95 percent of the time, there is a hard hose that breaks from the pump to the sencondary air injection pump. It causes a vacuum leak.

ttuling

for cracks in the hoses controlled by the solenoid valve at the back end of your broken hose. They're somewhat common, and the replacement hose has molded curved fittings which are less likely to crack where those hose bends.

In other words, follow your broken hose to the device (a solenoid valve) it plugs into toward the rear of the engine. Then follow the hose coming out of the side of the solenoid valve to the back of the engine. It plugs into a T fitting. From each side of the T, a hose goes to control a valve which lets secondary air into the exhaust for lower emissions during warm-up. These hoses from the T to the secondary air valves sometimes crack where they curve around to plug into the valve. Audi makes a more durable but expensive replacement, with the curve already molded into thicker end fittings, or you can use more of what's on there.

If you want to find vacuum hose with the same cloth covering as already on the car, a European import parts store should have it in bulk. I don't know if it's actually any more durable than the smooth surfaced stuff that everybody else sells.

Tom