I have a fluid mechanics question, that I think is caused by a lack of understanding of some key concepts. Suppose we have a horizontal capillary with a radius of 10um. The fabrication process has led to water having a contact angle of 110 degrees with 0.072N/m for the air-water surface energy. Based on the equation for capillary pressure we know that at least 4900Pa are needed to fill the tube.
My question is what happens when a 10cm column of water is connected to the capillary. Based on hydrostatics, this gives us a pressure of ~1000Pa, not enough to fill the horizontal capillary. What is the pressure when the vertical and horizontal sections meet? Is the pressure 1000Pa based on hydrostatics or is it 4900Pa due to the capillary pressure? It is my understanding that fluid pressure doesn't change along the horizontal under static conditions.
Thank you for taking the time to answer my question.