= You enter a competition to design an oil (Poil = 0.9 g/ml) and vinegar (Pvin...

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= You enter a competition to design an oil (Poil = 0.9 g/ml) and vinegar (Pvin = 1.3 g/ml) bottle. You know that oil and vinegar do not mix, so you come up with an amazing idea! Your design consists of an open-ended U-shaped tube, as in the figure above, with an inner diameter of d 5 cm. The bent part of the tube can hold 300ml of liquid. The straight parts are 15 cm high. You start by adding a volume V of vinegar to the tube, and then add oil until it reaches the top of one end of the tube without overflowing [Recall 1 ml hvin Oil hoil UU Balsamic Vinegar Balsamic Vinegar -H } 0.3 L = 1 cm]. (a) Write an expression for hvin, in terms of hoil, Poil, and Pvin. [Hint: Consider the pressure at the position marked by the red dashed line]. (b) Write an expression for the total volume V of vinegar in terms of hoil and hvin (c) Suppose that Vo = 500 ml. Using your answers from the previous parts, determine the maximum amount of oil (in ml) you can add to one end without the tube overflowing. [Hint: You have two equations and two unknowns]. ml = You enter a competition to design an oil (Poil = 0.9 g/ml) and vinegar (Pvin = 1.3 g/ml) bottle. You know that oil and vinegar do not mix, so you come up with an amazing idea! Your design consists of an open-ended U-shaped tube, as in the figure above, with an inner diameter of d 5 cm. The bent part of the tube can hold 300ml of liquid. The straight parts are 15 cm high. You start by adding a volume V of vinegar to the tube, and then add oil until it reaches the top of one end of the tube without overflowing [Recall 1 ml hvin Oil hoil UU Balsamic Vinegar Balsamic Vinegar -H } 0.3 L = 1 cm]. (a) Write an expression for hvin, in terms of hoil, Poil, and Pvin. [Hint: Consider the pressure at the position marked by the red dashed line]. (b) Write an expression for the total volume V of vinegar in terms of hoil and hvin (c) Suppose that Vo = 500 ml. Using your answers from the previous parts, determine the maximum amount of oil (in ml) you can add to one end without the tube overflowing. [Hint: You have two equations and two unknowns]. ml