# A Siphon at the Bar

**1. The problem statement, all variables and given/known data**

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 tall 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 has successfully designed a siphon.

Assume that the glass containing cranberry juice has a very large diameter with respect to the diameter of the straw and that the cross-sectional area of the straw is the same at all points. Let the atmospheric pressure be pa and assume that the cranberry juice has negligible viscosity.

Consider the end of the straw from which the cranberry juice is flowing into the glass containing orange juice, and let h0 be the distance below the surface of cranberry juice at which that end of the straw is located: (Figure 1) . What is the initial velocity v of the cranberry juice as it flows out of the straw? Let g denote the magnitude of the acceleration due to gravity.

**2. Relevant equations**

Bernoulli’s: [itex] p_1 + \frac{1}{2}\rho v_1^2+\rho gy_1 = p_2 + \frac{1}{2}\rho v_2^2 + \rho gy_2 [/itex]

**3. The attempt at a solution**

I tried using Bernoulli’s but I really don’t understand it at all. I’m bad with fluids, can anyone walk me through it?

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