内容发布更新时间 : 2024/5/5 21:26:54星期一 下面是文章的全部内容请认真阅读。

5.16 The velocity of a sphere depends on the sphere diameter, sphere density, fluid density, fluid viscosity, and gravitational acceleration：

Find a nondimensional form for the velocity.

一球体的速度与球体的直径、球体的密度、流体的密度、流体的粘度及重力加速度有关： 试导出速度的无量纲表达式。(

5.17 The pressure drop in a smooth horizontal pipe in a turbulent, incompressible flow depends on the pipe diameter, pipe length, fluid velocity, fluid density, and dynamic viscosity:

Find a nondimensional relationship for the pressure drop.

一水平放置光滑管道内不可压缩流体的湍流压降与管道直径、管长、流体速度、流体密度及动力粘度有关： 求压降的无量纲关系式。(

5.18 A small ball is dropped into a large tube containing an incompressible, viscous liquid. Experimental results show that the resistance force FD acted on the ball is related to the diameter D, velocity of the ball v, the fluid density ?, and viscosity ? of the fluid. Derive an expression for the resistance force FD.

一小球掉入盛有不可压缩的粘性液体的大管道中。实验结果表明，作用在小球上的阻力FD与小球的直径D、速度v、流体的密度?及粘度?有关。导出阻力FD的表达式。(FD=k?D2v2f(Re))

5.19 Experimental results show that the flowrate qv across an orifice meter is related to the pressure difference ?p between the upstream and downstream sides of the orifice, diameter D of the pipe, viscosity ? and density ? of the fluid. Using the Buckingham ? theorem to derive an expression for the flowrate q.

实验结果表明，孔口流量计的流量qv与孔口上下游的压差?p、管道直径D、流体的粘度?及密度?有关。试用帕金汉?定理导出流量qv的表达式。 (qv?kD?f(D2?p??2))

vt?tp)

)

Problems

6.1 A fluid flows in round pipe of diameter d=15mm at velocity v＝14m/s, determine the flow regime. In order to ensure that the flow is laminar flow, what is the maximum allowed velocity in the pipe for fluid of (1) lubricant ?＝l.0?10-4m2 /s; (2) water ?＝l.0?10-6m2 /s, and (3) air ?＝l.5?10-5m2 /s?

流体以v＝14m/s 的流速在直径 d＝15mm的圆管中流动，试确定流动状态。

(1) 润滑油?＝l.0?10-4m2 /s，(2) 水?＝l.0?10-6m2 若要保证流态为层流，对于流体：

/s，(3) 空气?＝l.5?10-5m2 /s，它们在管道中的最大允许速度各为多少？ ((1) 层流，15.47m/s (2) 湍流，0.155m/s (3) 湍流，2.32m/s)

6.2 Oil of density ?=740kg/m3 and dynamic viscosity ?＝4.03?10-3Pa?s flows in a horizontal round pipe of diameter d=2.54cm at an average velocity of v=0.3m/s. Calculate the pressure drop of oil along pipe of length l＝30m, and the oil velocity at place with distance of 0.6cm to pipe wall.

密度?=740kg/m3，动力粘度 ?＝4.03?10-3Pa?s的油液以平均流速v=0.3m/s流过直径 d=2.54cm的水平放置的圆管。试计算油液在l＝30m长的管道上的压强降，并计算距圆管内壁0.6cm处油液的流速。(1799Pa 0.433m/s)

6.3 The diameter and length of oil transporting pipe are d＝15cm, l＝5000m respectively, its outlet is h＝10m higher that inlet, oil transporting flowrate is qm＝15489kg/h, oil density is ?=859.4kg/m3, oil pressure at the inlet is pi＝49?104Pa, friction loss factor is ?=0.03, find the pressure pe at the outlet.

输油管的直径d＝15cm，长l＝5000m，出口端比入口端高h＝10m，输送油的流量 qm＝15489kg/h，油的密度?=859.4kg/m3，入口端的油压pi＝49?104Pa，沿程损失系数?=0.03，求出口端油压pe。(pe=3.712?105Pa)

6.4 A fluid flows through two horizontal pipes of equal length which are connected together to form a pipe of length 2l, as shown in Fig.6-30. The flow in pipes is laminar and fully developed. The pressure drop for the first pipe is 1.44 times greater than it is for the second. If the diameter of the first pipe is D, determine the diameter of the second pipe.

流体流过两根相互连接水平放置的长度皆为l的管道，如图6-30所示。管内流动为充分发展

的层流。第一根管上的压降是第二根的1.44倍。 Fig.6-30 Problem 6.4 如第一根管的直径为D，确定第二根管的直径。

6.5 As shown in Fig. 6-31, water flows from water tank A to storage tank B through a pipe of diameter d＝25mm and length l＝10m. If the gauge pressure of the water tank is p=1.96?105Pa, H1＝lm, H2＝5m, minor loss coefficients at inlet and outlet of the pipe are ?1=0.5 and ?4=1 respectively, for valve ?2＝4, for each elbow ?3＝0.2, friction loss factor is ?＝0.03, find the flowrate of water.

如图6－31所示，水沿直径d＝25mm，长l＝10m的管道，从水箱A流到储

水箱B。若水箱中的表压强p=1.96?105Pa，H1＝lm，H2＝5m，管道入口和出口的局部损失系数分别为?1=0.5、?4=1，阀门局部损失系数?2＝4，每个弯头的局部损失系数?3＝0.2，沿程损失系数?＝0.03，试求水的流量。

(qv=2.04?10-3m3/s)

6.6 There are 250 identical brass pipes in a vapour condenser are in parallel connection, total flowrate of condensed water through the pipes is 80L/s, water kinetic viscosity of water is ?＝l.3?10-6m2/s, the Reynolds number should not be less than 15000 in order to guarantee flow regime in brass pipe

is turbulent, what is the magnitude that the inner diameter of brass pipe should not exceed? Fig.6-31 Problem 6.5

一蒸汽冷凝器，内有250根完全相同 的黄铜管并联，通过管中的冷却水的总流量为80L/s，水的粘度为?＝l.3?10-6m2/s，为保证水在黄铜管中的流态为湍流，要求管中的雷诺数不得小于15000，问黄铜管的内径不得超过多少？(d?0.021m)

6.7 Water flows in pipe of radius r0, the flow regime is laminar flow. Find the distance r to the pipe axis at where the velocity just equals the average velocity.

水在半径为r0的管中流动，流态为层流。求流速恰好等于管内平均流速的位置与管轴之间的距离r等于多大？ (

2ro ) 2

6.8 A fluid flows through a pipe of radius R with Reynolds number of 100,000. At what location, r/R, does the fluid velocity equal the average velocity?

流体以雷诺数等于100,000流过半径为R的管道。问在何处r/R流体的流速刚好等于平均流速？

6.9 A water pipe of diameter d＝25cm, length l＝300m, and absolute roughness ?＝0.25mm. If given the flowrate qv＝95l/s, kinetic viscosity ?＝l.0?10-6m2/s, what is the friction loss?

水管直径d＝25cm，长l＝300m，绝对粗糙度?＝0.25mm，已知流量qv＝95l/s，

-62

运动粘度 ?＝l.0?10m /s，求沿程损失为多少？(4.61m水柱)

6.10 Water at 800C flows through a 120mm diameter pipe with an average velocity of 2m/s. If the pipe wall roughness is small enough so that it does not protrude through the laminar sublayer, the pipe can be considered as smooth. Approximately what is the largest roughness allowed to classify this pipe as smooth?

800C的水以2m/s的平均流速流过直径为120mm的管道。如果管壁的粗糙度

很小，没有延伸到层流底层，可认为管道是光滑管。问管道是光滑管的可容许的最大粗糙度大约为多少？

6.11 As shown in Fig.6-32, neglect minor loss, to ensure fluid flowrate in the siphon is qv＝10-3m3/s, determine: (1) when H=2m, l=44m, ?＝l.0?10-4m2 /s, ?=900kg/m3, what is d for ensuring laminar flow? (2) if the limitation vacuum on section A with a distance l/2 to the pipe inlet is pv=52 920Pa, what is the maximum allowed height Zmax of the siphon above the surface of upper oil storage pool?

如图6-32所示，不计局部损失，要保证虹吸管中液体的流量为qv＝10-3m3/s，试确定：(1) 当H=2m，l=44m，?＝l.0?10-4m2 /s，?=900kg/m3时，为保证层流，d应为多少？(2)若在距管进口l/2处的A断面上的极限真空为pv=52 920Pa，虹吸管在上面贮油池油面以上的最大允许高度

Zmax为多少？ Fig. 6-32 Problem 6.11

((1) 0.055m (2) 4.97m)

6.12 Water flows in a smooth plastic pipe of 200mm diameter at a flow rate of 0.1m3/s. Determine the friction factor ? for this flow.

水以0.1m3/s的流量在直径为200mm的塑料管中流动，试确定流动的沿程损失系数?。

6.13 Water flows from a tank along a vertical pipe of l＝2m and diameter d＝4m into atmosphere, as shown in Fig. 6-?. Neglect minor loss, friction loss factor is ?=0.04, find: (1) the relationship between the pressure at pipe’s initial section area A and the water level h in the tank, and the magnitude of h when the absolute pressure at A equals atmospheric pressure; (2) the relationship of the flowrate qv and the pipe length l, and the relationship that water level h satisfies when it does not change with l.

水从水箱沿着高l＝2m，直径d＝4m的竖直管道流入大气，如图所示。不计局部损失，并且沿程损失系数

?=0.04，试求：(1)管道起始断面A的压强与箱内水位h之间的关系式，并求当h为多少时，A处的绝对压强等 Fig.6-33 Problem 6.13 于大气压强；(2)流量qv与管长l的关系，并求出在水位 h满足什么关系时，将不随l而变化？

((1) pA?pa??g(?h?d)/(??d/l) h=1m (2) qv?h?d?4d22gd(h?l)

d??l? )

6.14 Air flows through the fine mesh gauze shown in Fig. 6-34 with an average velocity of 1.5m/s in the pipe. Determine the loss coefficient for the gauze.

空气在管道中以1.5m/s的平均流速通过如图6-34所示的细纱布。试确定纱布的损失系数。(56.7)

Fig.6-34 Problem 6.14

6.15 As shown in Fig.6-35, the heating furnace consumes heavy oil at a rate of qm=300kg/h, density and kinetic viscosity of oil are ?=880kg/m3 and ?＝25?10-6m2/s respectively, the pressurized oil tank is h＝8m above the sprayer’s axis, oil transporting pipe’s diameter is d＝25mm and length is l=30m. Find the gauge

pressure of heavy oil in front of the oil sprayer.

如图6-35所示，加热炉消耗qm=300kg/h的重油，重油的密度?=880kg/m3，运动粘度?＝25?10-6m2/s，压力油箱位于喷油器轴线以上h＝8m处，而输油管的直径d＝25mm，长l=30m。求

在喷油器前重油的表压强。( 62504Pa) Fig.6-35 Problem 6.15

6.16 Determine the pressure drop per 300m length of new 0.2m diameter horizontal cast iron water pipe when the average velocity is 1.7m/s.

确定直径为0.2m、长300m、平均流速为1.7m/s的水平放置铸铁水管上的压降。

6.17 As shown in Fig. 6-36, the lubricant consumption of the engine is qv＝0.4cm3/s, the lubricant is supplied to the lubricant housings via an oil pipe from the pressurized tank, the pipe’s diameter is d＝6mm and length is l＝5m. The density of the lubricant is ?=820kg/m3，and kinetic viscosity is ?＝15?10-6m2 /s. If the terminal pressure of the lubricant pipe equals atmospheric pressure, find the elevation h needed by the pressurized lubricant tank.

如图6-36所示，发动机润滑油的用量qv＝0.4cm3/s，