You're getting some confused answers. Hope I can help.
1. The fan you are replacing is fed from some power source in the case. I don't know whether it is a (manual) fan controller, or just straight from a 12 VDC PSU output. But I gather it has always run full speed. I see that it has only two wires to it and these are Black (Ground) and Red (+12 VDC). But the connectors involved are set up to accept standard 3-pin OR 4-pin fans, so replacement as you have done is no trouble at all.
2. What you have done WILL work. Since the power source you connect to has no connections for speed signal return (Pin #3) or for a PWM signal (Pin #4), the new fan will never feed its speed signal to any circuit that can read it, and the fan's speed will not be PWM controlled. Moreover, since the power supplied on Pin #2 is fixed, the fan's speed also cannot be altered under "Voltage Control Mode". Thus it will always run at full speed, exactly as the original one did. The point several posters have been trying to make is: if the new fan cannot be controlled in PWM Mode, why spend the money for that type of fan? But in terms of performance, yes, it will operate as a "normal" fan (of the 3-pin variety).
3. I see that your new fan has an unusual feature. In addition to the normal 4 wires coming out of it, it has a fifth Yellow wire that ends in a standard 3-pin fan connector, with the wire on Pin #3. Thus you COULD plug that into a mobo fan port and read the speed of this new fan via that mobo port if you wish. Of course, with your setup the speed will not change, but you could do that. One port you could use for that, IF your mobo has it, is called "PWR_FAN". If you want to do that, post back here and I'll give you more info.
4. You have not been using a "Molex splitter", so don't worry about that. What you did have in the old fan was a cable that had both a female connector to plug into the power source, and a male connector to be used as a new power source connection for a second similar fan (that you did not have). This cable acts like a "Y-splitter" because it allows you to connect two fans to one power source.
5. Several posters have been advising you how to connect the new fan to some mobo port so it can be put under "Automatic" speed control. That certainly could be done if you want to. Moreover, it could work no matter whether your mobo fan port is 3-pin or 4-pin. The way that backward compatibility in the designs of such fans works (when plugged into the "wrong" port type) is this: a 3-pin fan on a 4-pin port will always run full speed, but a 4-pin fan on a 3-pin port (THIS is your potential situation) WILL work with speed control. (In the latter case, control just will be done under Voltage Control Mode like a 3-pin fan, and not using the more advanced PWM Mode.) HOWEVER, you probably do not want to do this! "Automatic" control of a case ventilation fan speed by a mobo fan port is based on trying to achieve a measured temperature at a sensor built into the mobo by its maker. It is focused on the temperature of certain mobo components. BUT your concern is the temperature of your HARD DRIVE. There is NO automatic fan speed control system that is based on hard drive internal temperatures. Since you want to reduce your HDD's temperature by increasing the air flow over it, you are best to keep the new fan running at maximum speed using its full 12VDC power.
6. The proof will be in your temperature of the HDD, which you can measure somehow. But don't concentrate on the fan speed. What is important is the AIR FLOW the fan delivers, and speed is only one factor. Anything you can do to get more air flow (maybe less junk in the air flow path before or after the fan and HDD) will help. And make VERY sure that any dust filter mounted in front of the fan has been cleaned, and that you keep checking and re-cleaning it.
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