graphs four particles in s shown in Fig. P4.10. The Ar 0.002 s. The location the photos, are shown in th city for these particles. (b) s of part (a) with the the + ax), where a is the far from the sphere. xat 0.002s (n)
graphs four particles in s shown in Fig. P4.10. The Ar 0.002 s. The location the photos, are shown in th city for these particles. (b) s of part (a) with the the + ax), where a is the far from the sphere. xat 0.002s (n)
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Transcription for Educational Website:**
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**Section 4.10**
(Refer to "Fluids in the News" article titled "Follow those particles," Section 4.1.) Two photographs of four particles in a flow past a sphere are superimposed as shown in Fig. P4.10. The time interval between the photos is \(\Delta t = 0.002 \, \text{s}\). The locations of the particles, as determined from the photos, are shown in the table.
**Task:**
(a) Determine the fluid velocity for these particles.
(b) Plot a graph to compare the results of part (a) with the theoretical velocity, which is given by \(V = V_0 (1 + a^2/x^2)\), where \(a\) is the sphere radius and \(V_0\) is the fluid speed far from the sphere.
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**Data Table:**
| Particle | \(x \, \text{at} \, t = 0 \, \text{s} \, (\text{ft})\) | \(x \, \text{at} \, t = 0.002 \, \text{s} \, (\text{ft})\) |
|----------|--------------------------|--------------------------------|
| 1 | -0.500 | -0.480 |
| 2 | -0.280 | -0.260 |
| 3 | -0.140 | -0.128 |
| 4 | -0.060 | 0.112 |
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**Diagram Description:**
- **Figure P4.10** provides a visual representation of the experiment.
- The particles' positions at two different times are marked along a horizontal axis.
- The axis includes a sphere, depicted centrally, with distances marked on either side to indicate the positions of particles at the given time intervals, illustrating their movement relative to the sphere.
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