What is the maximum DC voltage you could expect to obtain from a transformer with an 18V rms secondary using a bridge rectifier circuit with a filter capacitor?

The maximum DC voltage you could expect to obtain from a transformer with an 18V rms secondary using a bridge rectifier circuit with a filter capacitor is about 24V.

This assumes a truly sinusoidal AC waveform, and a forward conductioin voltage of 0.7 volts across each diode.

Multiply 18 by the square root of two, and subtract two times the diode voltage.

The maximum is the peak value. If there is any load on the output, there will be some ripple, but the peak value will still be around 24V.

To calculate the output voltage of single phase diode bridge it is reasonable to assume a filter capacitor exists across the output and realize that it will be charged to the maximum voltage available to it.