Jane goes to a juice bar with her friend Neil. She is thinking of ordering her favorite drink, 7/8 orange juice and 1/8 cranberry juice, but the drink is not on the menu, so she decides to order a glass of orange juice and a glass of cranberry juice and do the mixing herself. The drinks come in two identical glasses to avoid spilling while mixing the two juices. Jane shows Neil something she learned that day in class. She drinks about 1/8 of the orange juice, then takes the straw from the glass containing cranberry juice, sucks up just enough cranberry juice to fill the straw, and while covering the top of the straw with her thumb, carefully bends the straw and places the end over the orange juice glass. After she releases her thumb, the cranberry juice flows through the straw into the orange juice glass. Jane successfully designed a siphon.
Find the time it takes Jane to transfer enough cranberry juice into the orange juice glass to make her favorite drink if . Assume that the flow rate of the liquid is constant, and that the glasses are cylindrical with a diameter of 7.0 centimeters and are filled to aheight of 14.0 centimeters. Take the diameter of the straw to be 0.4 centimeters. Â