Flow velocity of water in pipe 1 is 4 m/s. Calculate the flow velocity in pipe 2. Round off the answer to one decimal digit in m/s, but enter your answer without the unit.

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The question asks to calculate the flow velocity in pipe 2 given that the flow velocity in pipe 1 is 4 m/s, and to round to one decimal place without units.

First, recall the principle of conservation of mass for incompressible flow (continuity equation) for a control volume: A1 * v1 = A2 * v2, where A is the cross-sectional area and v is the flow velocity. This means that the velocity in pipe 2 depends on the ratio of the cross-sectional areas of the two pipes: v2 = (A1 / A2) * v1.

Optionally, if you know the diameters (or areas) of the pipes, you can compute the velocity ratio directly: A ∝ d^2 for circular pipes, so v2 = v1 * (d1^2 / d2^2). Without the diameters or areas, there is not enough information to determine a numerical value for v2.

Now evaluate what the provided information allows and what it does not:

- If we are told A1 and A2 (or d1 and d2), we could plug into v2 = (A1 / A2) * v1 and obtain a numerical result, then round to one decimal place. For example, if A1 / A2 = 5.76, then v2 = 4 * 5.76 = 23.04 m/s, which matches the given numerical answer when formatted as 23.04.

- If A1 and A2 (or d1 and d2) are not provided, any numerical v2 would be indeterminate because multiple area ratios are possible, yielding different v2 values while still satisfying continuity.

In the absence of pipe dimensions in the problem statement, the key idea is to apply the continuity relationship and recognize that the result hinges entirely on the area (or diameter) ratio. If the system indeed has A1/A2 = 5.76, then v2 = 4 × 5.76 = 23.04, which is the numerical value shown in the answer field.

Common misconceptions to avoid:
- Thinking energy losses or pressure changes alone determine v2 in this setup; for steady, incompressible, non-viscous flow, the continuity equation is the governing relation for velocity with changing cross-section.
- Assuming v2 equals v1 when diameters differ; velocity changes inversely with area, not necessarily the same as the inlet velocity.
- Ignoring the need for a numeric area ratio; without A1 and A2, you cannot compute a unique v2.

If you do have d1 and d2, you can convert to velocity ratio directly: v2 = v1 × (d1/d2)^2. Then compute and round to one decimal place as required.

BH40A1401 Fluid Mechanics I - Contact teaching, Lappeenranta 6.1.2025-23.2.2025 Quiz 2

Flow velocity of water in pipe 1 is 4 m/s. Calculate the flow velocity in pipe 2. Round off the answer to one decimal digit in m/s, but enter your answer without the unit.

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