Why single phase fan1 speed is > fan2

You didn't state the rpm of your friend's fan. Maybe it is wound with fewer poles, thereby turning faster. Also, the blade pitch and diameter could differ from your fan. I would expect 80W to do somewhat, but not greatly, more air flow than 75W.

I could not measure the rpm, it was easily feeling that the fan was running fast as compare with my fan.

With one formula, you can find what fan is right for your home. This is the formula for fan CFM: Cubic feet per minute, more commonly known as CFM is calculated by the following formula: air speed (feet per minute) X area (square feet)=CFM. Not everyone is going to take a look at CFM, but for those who do it is a helpful tool. In simpler words than that of the formula, it is the amount of air a fan moves.

The amount of air depends on some other factors as well, such as the diameter and shape of the blades, speed at which the blades turn (revolutions per minute or rpm), horsepower (hp) of the motor, and overall fan design. These combined factors establish the air moving capacity of a fan. Fan capacity is measured in terms of the cubic feet, and again, this is how CFM (cubic feet per minute is determined.)

Hope this will help.........

80 watt versus 75 watt, I would be inclined to assume that the 80 watt fan would run slightly faster.

Being that you can not establish the RPM of your friend's fan but can only feel the difference, have you taken into consideration that there may be other contributing factors such as difference in blade pitch, mounting distance from ceiling and/or floor, room size, ect, ect?

Just a couple thoughts.

Many ceiling fans are shaded pole motors, not capacitor start. The design of the motor itself and the blade pitch (load on the motor) will determine the running speed. These are often "impedance limited" motors so they can be completely stalled without over loading, so even if the motors are exactly identical, increasing the load by having a different blade pitch will result in a different running speed, but it will draw more current. 75W vs 80W may indicate that exact difference.

The most useful information would be to compare the RPM of the two motors, but since you do not have this information you could try swapping blades between the two fans and see which fan moves more air.

A blade with little pitch would reduce the load on the motor and allow the fan to spin at nearly 100% of the motor's rated speed. This would make you feel more movement of air, but only when you are directly below the fan. With greater pitch on the blades roughly the same amount of air is moved, but it is spread out more evenly throughout the room.

Ok.

In three phase motor, the rpm is related with frequency and poles of motor, then what about single phase motors? how we calculate their speed?

It is an un-understandable for me that in some cases, we connected the higher rated capacitor as compare with original and found the speed of single phase fan increased.

You can vary the speed of a single phase motor by manipulating voltage to the motor which is probably how your fan works, but care must be taken when you do so to ensure that the resulting change in torque does not over-load the motor's windings. Other common ways to vary speed of a single-phase motor are to energize more windings, space the windings closer together, or use pulley ratios and belts.

Most of the time a capacitor on a single phase motor only serves to increase torque output during startup, but in applications where there is only a small continuous load on the motor (like a fan) a permanent split capacitor (PSC) can be wired to improve the efficiency of the motor.

Here's a wiring diagram for a typical ceiling fan from http://www.educypedia.be/electronics/motoracsingle.htm

*Notice that on low and medium speeds the Autotransformer is in series with the fan motor. This changes the voltage drop across the motor windings.

The PSC is supposed to be sized to null the "power lag" created by the inductance of the motor's windings in order to get the efficiency of the motor to near unity (current and voltage 100% in phase). Over-sizing the capacitor too much will create a "power lead" which may affect the motor's speed but at the expense of efficiency.

The applications of "power lead" and "lag" are very "un-understandable" even if you have the equations. The discipline of "Power Engineering" is centered around this. For more information you can Google "apparent power" or follow this link: http://en.wikipedia.org/wiki/AC_power