Water will only flow across a membrane firstly if the membrane is permeable to water. There is no such thing as water flow across an impermeable plastic membrane!
Now, we need to determine what factors would cause water to flow across a permeable membrane. Generally, these factors are based on two things: hydrostatic pressure and osmotic pressure.
Hydrostatic pressure would cause water to flow from an area of high pressure to an area of low pressure. For example, if you pressurize the tank of a squirt gun and pull the trigger, the elevated pressure in the tank relative to outside the gun causes water to flow onto the person you are squirting. The same principle causes water to flow across membranes in the body in heart failure, causing pulmonary edema in the lungs.
Osmosis is based on a different principle. If you have different solute concentrations across a membrane, and those solutes are unable to cross, then water will cross to even out the osmolarity. For example, if you have a tank with a high concentration of protein mixed in water connected to a tank with a lower concentration of protein, then water will flow from the lower concentration to the higher concentration until the concentrations are equal. A good example of this is when you put cells into a highly concentrated salt solution. Water will flow out of the cells and cause them to shrivel. Conversely, if you put cells into water with a very low salt concentration, water may flow into the cells to the point of bursting!