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EXAMPLE 4-2 Acceleration of a Fluid Particle through a Nozzle Nadeen is washing her car, using a nozzle similar to the one sketched in Fig. 4-8. The nozzle is 3.90 in (0.325 ft) long, with an inlet diameter of 0.420 in (0.0350 ft) and an outlet diameter of 0.182 in (see Fig. 4-9). The volume flow rate through the garden hose (and through the nozzle) is V = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate the magnitude of the acceleration of a fluid particle moving down the centerline of the nozzle.

EXAMPLE 4-2 Acceleration of a Fluid Particle through a Nozzle Nadeen is washing her car, using a nozzle similar to the one sketched in Fig. 4-8. The nozzle is 3.90 in (0.325 ft) long, with an inlet diameter of 0.420 in (0.0350 ft) and an outlet diameter of 0.182 in (see Fig. 4-9). The volume flow rate through the garden hose (and through the nozzle) is V = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate the magnitude of the acceleration of a fluid particle moving down the centerline of the nozzle.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the point of view of a fixed observer ticles may accelerate, even in a steady flow. In this example, the exit speed of the water is much higher than the water speed in the hose, implying that ates as it passes through the nozzle. fluid particles have accelerated even though the flow is steady. in the Eulerian reference frame, it is not steady from the Lagrangian refer- ence frame moving with a fluid particle that enters the nozzle and acceler- EXAMPLE 4–2 Acceleration of a Fluid Particle through a Nozzle i Nadeen is washing her car, using a nozzle similar to the one sketched ini Fig. 4-8. The nozzle is 3.90 in (0.325 ft) long, with an inlet diameter of ▪ 0.420 in (0.0350 ft) and an outlet diameter of 0.182 in (see Fig. 4-9). The volume flow rate through the garden hose (and through the nozzle) is V = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate the magnitude of the acceleration of a fluid particle moving down the centerline of the nozzle. SOLUTION The acceleration following a fluid particle down the center of a nozzle is to be estimated. Assumptions 1 The flow is steady and incompressible. 2 The x-direction is taken along the centerline of the nozzle. 3 By symmetry, v = w = 0 along the centerline, but u increases through the nozzle. Analysis The flow is steady, so you may be tempted to say that the accel- eration is zero. However, even though the local acceleration aVlat is identi- cally zero for this steady flow field, the advective acceleration (V.V)V is not zero. We first calculate the average x-component of velocity at the inlet and outlet of the nozzle by dividing volume flow rate by cross-sectional area: Hudet Inlet speed: Doutet <) (> 1.44 (+ =小中 A File - Tools - 163 freepdfsolutions.com O Search 4:47 AM ^ L )5/23/2021
Transcribed Image Text:A Fluid Mechanics, Third Edition - Free PDF Reader E3 Thumbnails 138 FLUID KINEMATICS Fluid Mechanies Fundamenteis and Applicationu acceleration); this term can be nonzero even for steady flows. It accounts for the effect of the fluid particle moving (advecting or convecting) to a new location in the flow, where the velocity field is different. For example, nunan A Çengel | John M. Cinbala consider steady flow of water through a garden hose nozzle (Fig. 4-8). We define steady in the Eulerian frame of reference to be when properties at any point in the flow field do not change with respect to time. Since the velocity at the exit of the nozzle is larger than that at the nozzle entrance, fluid particles clearly accelerate, even though the flow is steady. The accel- eration is nonzero because of the advective acceleration terms in Eq. 4-9. FLUID MECHANICS FIGURE 4-8 Flow of water through the nozzle of a garden hose illustrates that fluid par- Note that while the flow is steady from the point of view of a fixed observer ticles may accelerate, even in a steady flow. In this example, the exit speed of the water is much higher than the water speed in the hose, implying that ates as it passes through the nozzle. fluid particles have accelerated even though the flow is steady. in the Eulerian reference frame, it is not steady from the Lagrangian refer- ence frame moving with a fluid particle that enters the nozzle and acceler- EXAMPLE 4–2 Acceleration of a Fluid Particle through a Nozzle i Nadeen is washing her car, using a nozzle similar to the one sketched ini Fig. 4-8. The nozzle is 3.90 in (0.325 ft) long, with an inlet diameter of ▪ 0.420 in (0.0350 ft) and an outlet diameter of 0.182 in (see Fig. 4-9). The volume flow rate through the garden hose (and through the nozzle) is V = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate the magnitude of the acceleration of a fluid particle moving down the centerline of the nozzle. SOLUTION The acceleration following a fluid particle down the center of a nozzle is to be estimated. Assumptions 1 The flow is steady and incompressible. 2 The x-direction is taken along the centerline of the nozzle. 3 By symmetry, v = w = 0 along the centerline, but u increases through the nozzle. Analysis The flow is steady, so you may be tempted to say that the accel- eration is zero. However, even though the local acceleration aVlat is identi- cally zero for this steady flow field, the advective acceleration (V.V)V is not zero. We first calculate the average x-component of velocity at the inlet and outlet of the nozzle by dividing volume flow rate by cross-sectional area: Hudet Inlet speed: Doutet <) (> 1.44 (+ =小中 A File - Tools - 163 freepdfsolutions.com O Search 4:47 AM ^ L )5/23/2021
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