5.11 A 1:49 scale model of a ship is tested in a water tank. The speed of the prototype is 10m/s. The purpose of the test is to measure the wave drag on the ship. Find the velocity of the model and the ratio of the wave drag on the prototype to that on the model.

一比尺为的船模在水池中实验。原型中的速度为10m/s。实验的目的是测定作用在船上的波浪阻力。求模型的速度，及原型与模型的波浪阻力比值。 (1.43 m/s，1.18?105)

5.12 A Venturi tube with diameter D1=300mm and d1=150mm is used to measure the flowrate of oil of kinematic viscosity ?1=4.5?10-6m2/s and density ?1=820kg/m3. The flowrate Q1 is 100L/s. Use water of kinematic viscosity ?2=1?10-6m2/s and a 1:3 model to perform the test.

(1) What must the water flow rate Q2 be for dynamic similarity?

(2) If the head loss hf2 is measured at 0.2m and the pressure difference ?p2 at 1.0 bar in the model test, find the real head loss and pressure difference of the prototype. 一直径为D1=300mm 及 d1=150mm的文丘里管用于测量运动粘度为?1=4.5?10-6m2/s、密度为?1=820kg/m3的油的流量。流量Q1 为100L/s。用运动粘度为?2=1?10-6m2/s的水、比尺为1:3的模型进行实验。

(1) 为了达到动力相似，水的流量Q2为多少？

(2) 如果模型实验测得水头损失hf2为0.2m、压差?p2为1.0 bar，求原型的水 头损失与压差为多少。?

5.13 The flowrate qv of a fluid passing through a horizontal capillary pipe has relationship with the diameter d, dynamic viscosity ? and pressure gradient ?p/l, derive the expression of the flowrate.

流体通过水平毛细管的流量qv与管径d、动力粘度?、压强梯度?p/l有关，试导出流量的表达式。(

)

5.14 A small ball travels at a constant velocity in an incompressible viscous fluid, the drag is related with the diameter of the ball, velocity v, the density ? of the fluid, and the dynamic viscosity ?. Find the expression of the drag.

小球在不可压缩粘性流体中等速运动时，阻力FD与小球的直径d、运动速度v、( 流体密度?、动力粘度?有关，试推导出阻力的表达式。

)

5.15 The outlet velocity v of an orifice is related with the orifice diameter d, fluid density ?, dynamic viscosity ? and hydrostatic head ?p, derive the expression of the outlet velocity.

设孔口出流的速度v与孔口直径d、流体密度?、动力粘度?以及静压头?p有关，导出流速的表达式。(

)

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