In ancient Egypt the priests needed to tell the time during the  night, so  that the rites and sacrifices could be duly performed. On clear nights they could  use the stars to designate the hours, but they needed a clock when it was cloudy. The Egyptians had a water­clock for this purpose in their temples which made use of the flow of water through a fine orifice for time regulation. Since the Egyptians used a linear scale on the inside of their clocks to mark the hours, the  bottom of the vessel had to have a smaller cross­sectional area then the top.The submersive float  is  another type of time measuring device. It  was  used in Antiquity to determine a given time duration. A vessel with a fine ori­  fice on the bottom is put on a water surface. When the vessel sinks one knows  that a predetermined time has passed. If desired, one can pour out the water and  put the vessel for a second time on the water surface. If the vessel cross­section  is equal along the height of the vessel the sinking rate is constant, and time scale generally marked on the in­ or outside wall of the vessel is linear. This kind of time devices were in use from Antiquity till the beginning of twentieth century  to determine the lecturing time of a speaker or the irrigation time in agriculture.The most important work on engineering written before the Renaissance was  the book on mechanics Kitab  al­hiyal of Ibn al­Razzâz al­Jazari. It  was  composed in Diyarbakır (present  day Turkey) in 1206. There are 50  different  devices, such as water clocks, trick vessels, liquid dispensers, and phlebotomy  measuring instruments, fountains, musical  automata, and water­raising ma­ chines, as well as  a submersive float (tarjahar) like the one described above. This is a 1½ span­long (app.35 cm) sinking vessel in the form of an elegant boat  in which a boatman stands and plays a flute. The boat put on water surface sinks  after one hour and the boatman informs the end of the hour by blowing a tone.In this paper first, a detailed mathematical model of the outpouring and  sinking process is given. Secondly, a calculation method is developed and applied for the orifice diameter in the determination of the al­Jazari type time­ keeping vessel.

In ancient Egypt the priests needed to tell the time during the  night, so  that the rites and sacrifices could be duly performed. On clear nights they could  use the stars to designate the hours, but they needed a clock when it was cloudy. The Egyptians had a water­clock for this purpose in their temples which made use of the flow of water through a fine orifice for time regulation. Since the Egyptians used a linear scale on the inside of their clocks to mark the hours, the  bottom of the vessel had to have a smaller cross­sectional area then the top.The submersive float  is  another type of time measuring device. It  was  used in Antiquity to determine a given time duration. A vessel with a fine ori­  fice on the bottom is put on a water surface. When the vessel sinks one knows  that a predetermined time has passed. If desired, one can pour out the water and  put the vessel for a second time on the water surface. If the vessel cross­section  is equal along the height of the vessel the sinking rate is constant, and time scale generally marked on the in­ or outside wall of the vessel is linear. This kind of time devices were in use from Antiquity till the beginning of twentieth century  to determine the lecturing time of a speaker or the irrigation time in agriculture.The most important work on engineering written before the Renaissance was  the book on mechanics Kitab  al­hiyal of Ibn al­Razzâz al­Jazari. It  was  composed in Diyarbakır (present  day Turkey) in 1206. There are 50  different  devices, such as water clocks, trick vessels, liquid dispensers, and phlebotomy  measuring instruments, fountains, musical  automata, and water­raising ma­ chines, as well as  a submersive float (tarjahar) like the one described above. This is a 1½ span­long (app.35 cm) sinking vessel in the form of an elegant boat  in which a boatman stands and plays a flute. The boat put on water surface sinks  after one hour and the boatman informs the end of the hour by blowing a tone.In this paper first, a detailed mathematical model of the outpouring and  sinking process is given. Secondly, a calculation method is developed and applied for the orifice diameter in the determination of the al­Jazari type time­ keeping vessel.