Normally people could open eyes under water, but whether it is harmful is depending on what kind of water you mean by. If it is absolutely clean, it should be ok to open eyes in it. There is such method and production medically to help people wash eyes. However, if you are trying to open your eyes in swimming pool or someplace like this, I am afraid it is not a good idea. Water in swimming pool contains various bacteria and disinfectant, which could be very irritated to eyes. Although ears produced by eyes could kill 90-95% bacteria in eyes, yet there is still 5-10% left which can't be killed. Many people got conjunctivitis because swimming in public pool. I, myself, could help closing my eyes in swimming pool when I was under water. This is the so called unconsciously active response to protect eyes. wearing swimming goggles is much better than not.