Question: You are developing a system that will use a reduced pipe diameter as a way to draw in a very small amount of liquid chocolate

 You are developing a system that will use a reduced pipe

You are developing a system that will use a reduced pipe diameter as a way to draw in a very small amount of liquid chocolate from a reservoir in order to make chocolate milk. Whole milk flows from a very large, open storage tank through a pipe with diameter 0.105m, dropping 11.710m before entering a pipe reduction. The pipe diameter is reduced to 0.078m, then liquid chocolate is added through a 0.011m inner diameter pipe from a very large pressurized tank with some height of liquid in it. Then, the pipe expands back to its original diameter (0.105m) and releases the finished product into the atmosphere (101560 Pa), where it falls into another storage tank for future processing and shipment to customers. Both milk and liquid chocolate have a density of 1208 kg/m3. If the height of chocolate that needs to be maintained in the pressurized tank to achieve a mixture of only 3.96 percent chocolate and the rest normal milk is 0.850m, calculate the required Pt in Pa. Neglect frictional losses. (Hint: assume the flow rate of milk is not affected by adding such a small amount of chocolate)

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