The rear washer stopped working on my 2011 i30. I eventually traced it to an inline hose coupler which is visible if you pull down the roof lining at the rear. It incorporates what looks like a non-return valve, with a spring inside, and a tiny piston and rubber washer. The valve didn't allow any flow in either direction, so I removed all the insides, re-connected the hoses and it now works fine. I thought the tube had a blockage so tried clearing it with a foot-pump, but all this did was to blow the tube off the coupler and push the residual fluid in the tube into the head lining.
If one washer is working, remove the wheel arch lining to gain access to the washer pump, and try swapping the washer pipes at the pump. For example, if the front washer works but not the rear washer, try the front washer and it should squirt on the rear screen. If it still doesn't work, it suggests the pump is healthy and the fault lies with the pipework.
