A Fluid Mechanics, Third Edition - Free PDF ReaderE3Thumbnails138FLUID KINEMATICSFluid MechaniesFundamenteis and Applicationuacceleration); this term can be nonzero even for steady flows. It accountsfor the effect of the fluid particle moving (advecting or convecting) to anew location in the flow, where the velocity field is different. For example,nunan A Çengel | John M. Cinbalaconsider steady flow of water through a garden hose nozzle (Fig. 4-8). Wedefine steady in the Eulerian frame of reference to be when properties atany point in the flow field do not change with respect to time. Since thevelocity 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 MECHANICSFIGURE 4-8Flow of water through the nozzle ofa garden hose illustrates that fluid par- Note that while the flow is steady from the point of view of a fixed observerticles may accelerate, even in a steadyflow. In this example, the exit speedof the water is much higher than thewater speed in the hose, implying that ates as it passes through the nozzle.fluid particles have accelerated eventhough 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 4–2Acceleration of a Fluid Particle through a Nozzle iNadeen is washing her car, using a nozzle similar to the one sketched iniFig. 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) isV = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate themagnitude of the acceleration of a fluid particle moving down the centerlineof the nozzle.SOLUTION The acceleration following a fluid particle down the center of anozzle is to be estimated.Assumptions 1 The flow is steady and incompressible. 2 The x-direction istaken along the centerline of the nozzle. 3 By symmetry, v = w = 0 alongthe 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 notzero. We first calculate the average x-component of velocity at the inlet andoutlet of the nozzle by dividing volume flow rate by cross-sectional area:HudetInlet speed:Doutet1.44 (+=小中A File -Tools -163freepdfsolutions.comO Search4:47 AM^ L )5/23/2021

Question

A Fluid Mechanics, Third Edition - Free PDF ReaderE3Thumbnails138FLUID KINEMATICSFluid MechaniesFundamenteis and Applicationuacceleration); this term can be nonzero even for steady flows. It accountsfor the effect of the fluid particle moving (advecting or convecting) to anew location in the flow, where the velocity field is different. For example,nunan A Çengel | John M. Cinbalaconsider steady flow of water through a garden hose nozzle (Fig. 4-8). Wedefine steady in the Eulerian frame of reference to be when properties atany point in the flow field do not change with respect to time. Since thevelocity 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 MECHANICSFIGURE 4-8Flow of water through the nozzle ofa garden hose illustrates that fluid par- Note that while the flow is steady from the point of view of a fixed observerticles may accelerate, even in a steadyflow. In this example, the exit speedof the water is much higher than thewater speed in the hose, implying that ates as it passes through the nozzle.fluid particles have accelerated eventhough 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 4–2Acceleration of a Fluid Particle through a Nozzle iNadeen is washing her car, using a nozzle similar to the one sketched iniFig. 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) isV = 0.841 gal/min (0.00187 ft/s), and the flow is steady. Estimate themagnitude of the acceleration of a fluid particle moving down the centerlineof the nozzle.SOLUTION The acceleration following a fluid particle down the center of anozzle is to be estimated.Assumptions 1 The flow is steady and incompressible. 2 The x-direction istaken along the centerline of the nozzle. 3 By symmetry, v = w = 0 alongthe 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 notzero. We first calculate the average x-component of velocity at the inlet andoutlet of the nozzle by dividing volume flow rate by cross-sectional area:HudetInlet speed:Doutet<) (>1.44 (+=小中A File -Tools -163freepdfsolutions.comO Search4:47 AM^ L )5/23/2021

Accepted Answer

Considering the motion in the nozzle as steady, one-dimensional incompressible flow. The velocity of…