As you raise the Mariotte bottle, the pressure head on the inflow SIDE of the column increases and the WATER flows out faster. Total head, which is the gravity head plus pressure head in this system is higher when the Mariotte bottle is raised. According to Darcy’s law, the rate of flow is a function of the cross SECTIONAL area, the hydraulic conductivity, and the potential gradient. By INCREASING the gradient (the difference in head at the inflow and outflow ENDS of the column) we increase the flow rate. 

As you raise the Mariotte bottle, the pressure head on the inflow side of the column increases and the water flows out faster. Total head, which is the gravity head plus pressure head in this system is higher when the Mariotte bottle is raised. According to Darcy’s law, the rate of flow is a function of the cross sectional area, the hydraulic conductivity, and the potential gradient. By increasing the gradient (the difference in head at the inflow and outflow ends of the column) we increase the flow rate.