Water clocks were an example of early innovation made in different parts of the world with China, Egypt, Babylon, India and eventually Greece utilizing them for time and astrology. The earliest water clocks used by the Greeks were simple. Water was filled in a bowl or a clepsydra to the top and a spout led to another bowl which counted the time in hours with markings. The water would flow out slower when the pressure decreased so they made special markings on the receiving bowl to account for this. This was only a timer though. The Greeks made these simple to measure the time for defence of a court case or for example your time paid for with a prostitute. Several physical factors made these clocks and the future water clocks not precise.
The physical phenomena of gravity, viscosity and surface tension allows for the water clock to maintain a more precise time (although not in today's standards). The flow rate is inversely proportional to the viscosity both of which is dependent on the temperature. The surface tension affects the meniscus on the incoming water so an hour would never be really precise at the different temperatures (for example the water would run seven times faster at 100 C than at 0 C). The surface tension of the water would also affect the later made mechanical clocks which did not rely on a constant flow but rather added the water to another tank in drops. So any dust, soap, change in temperature could make the clock a lot slower.