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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)

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Transcription for Educational Website:** --- **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. --- **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 | --- **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.
Transcribed Image Text:**Transcription for Educational Website:** --- **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. --- **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 | --- **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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Given:-∆t=0.002secTo find:-fluid velocity 

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