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Fluid travels through a tube of adjustable diameter. Initially the diameter is 6.4 mm and the flow rate 1.08 L/min. (Assume that △P remains constant). How would the flow rate change if the diameter was changed to 7.0 mm ? If you wanted to reduce the flow rate through the tube by 40%, how would you adjust the diameter?

User Amit Kaspi
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Final answer:

When the diameter of a tube is changed, the flow rate of the fluid also changes. In this case, changing the diameter from 6.4 mm to 7.0 mm would result in a flow rate of 1.51 L/min.

Step-by-step explanation:

The flow rate of a fluid through a tube is directly related to the diameter of the tube. When the diameter is changed, the flow rate will also change. The relationship between flow rate and diameter is inversely proportional, meaning that as the diameter increases, the flow rate will decrease and vice versa.

In this case, we can calculate how the flow rate changes when the diameter is changed from 6.4 mm to 7.0 mm.

We can use the formula Q1/Q2 = A2/A1 = (D2/D1)²

Where

Q1 is the initial flow rate

Q2 is the new flow rate

A1 is the initial cross-sectional area

A2 is the new cross-sectional area

D1 is the initial diameter

D2 is the new diameter.

By plugging in the values, we get Q2 = Q1 * (D2/D1)² = 1.08 L/min * (7.0 mm/6.4 mm)² = 1.51 L/min.

So therefore the diameter from 6.4 mm to 7.0 mm would result in a flow rate of 1.51 L/min.

User Daniel Ives
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