Electronic – Choosing proper size of solenoid valve

It's ampere-turns that produce the magnetic field to attract the moving part of a solenoid and operating at AC means the inductance of the coil comes into play and there is a limiting impedance restricting current. At DC the solenoid dc resistance may be very low and to get it to work correctly might mean operating it at quite low dc voltages compared to the ac operating voltage.

If you try running it at 24V dc it could easily burn-out so be careful. The dc voltage should be chosen so that the current is approximately the same as the RMS ac current at 24V AC.

It's most likely a motorised valve.

Figure 1. Motorised valve attached to water hose line.

An industrial version of a motorised valve would have feedback potentiometer so that the actual position of the valve could be confirmed and, perhaps, proportional control could be achieved. Alternatively limit switches could be fitted to stop the motor once full travel had been reached.

In this case and in the case of the garden hose timers you linked I suspect that the motor would be run for a time and if the valve doesn't move then "too bad". With five or ten cycles per day the run time would only be half a minute or so and battery life should be good.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 2. Simplified representation of control circuit for open / close control including optional limit switches. With SW1 and SW4 closed as shown the motor would run CW until the CW limit switch opened.

Figure 2 shows how a simple DC motor would be switched by a 'H-bridge' to effect forward and reverse motion. SW1 to SW4 would, in a practical circuit, be replaced by transistors (with protection diodes).