The answer is not as simple. However, the bottomline is that the tube size determines the available surface per unit length as well as the pumping power requirements. They go in opposite directioons. However, other HX factors such a the pitch, pressure drop as well as mechanical factors affect the choice of the tube size
Yes, the surface area for heat transfer and pressure drop are two most important deciding factors. The expressions are available through which you can relate Nusselt, Reynolds and Prandtl numbers. There are papers / books available which you may see before starting the design iterations.
I agree with all above answers, and I recommend to see te book Heat Exhangers, Selection, Rating and Thermal Design, by authors: Sadik Kakac and Hongtan Lui, CRC Press!
The size of the tube depends on various parameters. It depends on the shell ID, the heat load, the tube pitch, tube length, number of baffles, the liquid properties and flow rate on the shell side, etc. You can refer to the book stated by Dr.Antun Galovic. You may also refer Process Heat Transfer by D.Q.Kern published by McGraw Hill. You have a number of worked out examples which can help you arrive at the tube size for your input parameters and process conditions.
You could start from defining your requirements (diameter, P/D, etc...) coming from mechanical and technological limits (maximum stress, minimum space you need to install and inspect the tubes, etc...).
Then once you know the range of your diameter you can size the number of tubes and the tube size according the power you need to remove, with an eye on pressure drops on both shell and tube sides.
There is the correct way which means following the quite lengthy procedure of designing a shell-and-tube HX which involves several trial-and-errors, and there is the garage-project way. Just to give you a quick answer (which is probably quite useless, scientifically speaking) for medium to larger heat duties, you will have to pick either 1/2" or 3/4" tube.
In order to select the tube size we need to study convective heat transfer and viscous fluid flow. Inlet length, Reynolds and Prandtl numbers are important parameters to select tube size. Steady state, laminar flow and constant properties are good assumptions for this problem.
Pressure drop and surface area for heat exchange. There are always recomendadtions for the maximum velocity of the fluid inside the tube bundel. For water is up to 1.5-2 m/s because of the pressure drop.
The answers of Taherian and Khaled come close. Mishra too is right. In GENERAL, you go for Re > 10,000, but not necessarily! If having a viscous oil in tubeside is inevitable, go for laminar flow. You have very limited range of choices for tube size, as they come in fixed sizes. (I do not know how or why this question escaped me!!!)
The most popular choices are 3/4" and 1". Occasionally, it goes down to 1/2" or up to
1-1/2" . Very very rarely even to 1/4" and 2", but I doubt you will encounter those extreme cases. With 3/4 or 1" and adjusting the tube pitch, baffle pitch, L/D etc., you can satisfy all other requirements like heat duty, pressure drop and space limitations.
the choosing of tube size depends on many factor such as fluid properties such as viscosity and density, what amount of heat transfer required, how many of tubes affecting the total area. in the same vein, there are standards diameter and length for tubes. you can follow kern's method for better understand.