fluid试卷及答案

 西安交通大学考试题 成绩 课 程 流体力学 (英文) 学 院 能动学院 考 试 日 期 2007 年 1 月 23 日 专业班号 能动41、42等 姓 名 学 号 期中 期末 √ Part Ⅰ Concepts 1. Fill in the blank (10×1.5) ① Classical Fluid Mechanics treats a fluid as an infinitely divisible substance, a continuum, and do not concern with the behavior of individual molecules. This is the so-called concept. ② Forces acting on the fluids are classified into two categories: forces act on the boundaries of a medium though direct contact. Forces developed without physical contact and distributed over the volume of the fluid are termed forces. ③ There are two distinct ways to describe fluid flow (to establish the equations of motion): approach specifies history of properties for individual fluid particles. For example, it is used to track discrete coal particles and droplets in a continuous fluid; approach focuses attention on the properties of a flow at a given point in space, which is based on field concept in a continuum and commonly used in analyzing fluid flow. ④ In pressure measurement, it is often convenient to take atmospheric pressure as a datum. Pressure measured above atmospheric pressure is known as pressure; pressure measured above perfect vacuum is called pressure. ⑤ Shock waves are typical for supersonic flows and cause irreversible losses of kinetic energy. Traditionally ‘shock waves’ are referred to wave (compression or expansion). Shock waves cause entropy (熵) (increase or decrease) ⑥ Streamline design is to delay the onset of flow separation and reduce drag. Generally speaking, the streamline-designed shape is longer-thinner or shorter-thicker? . 共 5 页 第 1 页

(注:从第2页起的双数页使用) rdVr⑦ Euler equation is written as ρ=ρg−∇p, and this equation is valid for dt flow. ⑧ Viscous flow regimes are classified as laminar or turbulent on the basis of flow structure. For pipe-flow, the flow regime is dependant on Reynolds number, and critical value of Reynolds number for transition to occur from laminar to turbulent is . The characteristic length (特征长度)of Reynolds number is herein taken as . ⑨ For internal viscous flow, development of boundary layer is restricted by the wall. When the boundary layer reaches the maximum extent, the profile shape no longer changes with increasing distance,x, the flow is termed ‘fully developed’. ⑩ The effect of friction is to decrease the pressure, causing a pressure “loss” compared to the ideal, frictionless flow case. Conventionally, the losses are divided into loss (due to friction in constant-area portion of the system), and loss (due to flow separation through valves, elbows, and other non-constant area of the system etc.). 2. Expressions and physical significance (5×5) z Write the expression of shear stress for the turbulent pipe flow, and explain the physical meanings of each term. Write the expression of sound speed(音速) for perfect gas; write the expression of Mach number(马赫数)；write expression of Reynolds number (雷诺数) and explain the physical meaning of Reynolds number. Write the mathematical definition of flow separation point; under what kind of pressure gradient, flow separation may possibly occur? Write the mathematical expression of fluid rotation velocity ω; give the condition for irrotational flow. Write the mathematical expression of acceleration for a fluid particle in translation motion (流体质点平移加速度)，and explain the physical meaning of each term r z z z z 第 2 页

西安交通大学考试题

(注:从第3页起的单数页使用)

Part Ⅱ Calculation and Analytical Problems

3. In the following figure, the water and gasoline surfaces are open to the atmosphere and at the same elevation. What is the height hof the third liquid in the right leg? (15)

Density of water ρwater=998kg/m3; density of gasolineρgasoline=680kg/m3; density of the third liquid is ρliquid=ρwater⋅SG

第 3 页

(注:从第2页起的双数页使用)

4. In the figure, the flowing fluid is CO2 at 20°. Neglect losses. If p1=170 kPa and the manometer fluid is Meriam red oil (SG=0.827), estimate

(a) p2

(b) The CO2 gas flow rate in m3/h

Density of CO2 is ρCO2=1.84 kg/m3 (15)

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西安交通大学考试题 (注:从第3页起的单数页使用) 5. An incompressible fluid flows past an impermeable (无渗透) flat plate, as in the following figure, with a uniform inlet profile u=U0 and a cubic polynomial exit profile 3η−η3u=U0() 2y Where η=δ Compute the volume flow Q across the top surface of the control volume. (15) (**Suggestion: Using the integral mass conservation law for fixed control volume and incompressible flow, i.e. ∑Q=∑Qinout) 6. Suppose that mathematical function f(x,y)＝2x2+xy−2y2 is stream function for a tow-dimensional flow field，please solve the following problems (1) Is this flow filed potential or irrotational flow (势流或无旋流动)？ (2) If fluid density ρ ＝ 1.12kg/m3 and at point (1m，-2m) flow pressure is 4800pa，try to obtain the pressure at point (－2m，1m). (15) 第 5 页

西安交通大学本科生课程考试试题标准答案与评分标准(A)

课程名称： 流体力学 (英文) 课时： 64 考试时间： 2007 年 1月 23 日

Part Ⅰ Concepts 1. Fill in the blank (10×1.5) ①; Continuum ② surface , body; ③ Lagrangian, Euler; ④ gage, absolute; ⑤ compression, increase; ⑥ longer-thiner; ⑦ inviscid; ⑧ 2300 or 2100, diameter; ⑨ velocity; ⑩ major, minor 说明：1）若用中文回答，答案正确不扣分 2）英文单词不唯一，酌情判分 2. Expressions and physical significance (5×5) 说明：1）若用中文回答，答案正确不扣分 2）英文单词不唯一，酌情判分 z Stress in turbulent flow τ=τviscous+τtur=μ∂u−ρu'v' ∂y = 粘性切应力＋紊流附加切应力 （3.5） 分别由粘性和随机脉动引起。 （1.5） z 1/2 a=(kRT) （1） M= Re=V (1) ainertia forceρVLVL== （1） μνviscous force 代表inertia force大小 (2) viscous forceSeparation point A critical condition where the wall shear being exactly zero is defined as the separation point, mathematically z ∂u/∂yy=0=0 (2.5) Adverse pressure gradient (逆压): ∂p/∂x>0 flow separation may occur (2.5) z i j krr1∂∂∂1ω=iωx+jωy+kωz= =∇×V 2∂x∂y∂z2u v w或 1∂w∂v−)2∂y∂z1∂u∂wωy=(−) 2∂z∂x1∂v∂uωz=(−)2∂x∂yωx=( (2.5) For irrotational flow i j krr1∂∂∂1ω=iωx+jωy+kωz= =∇×V=0 2∂x∂y∂z2u v w (2.5) z acceleration rrrrrrdV∂Vdx∂Vdy∂Vdz∂Va==+++dt∂xdt∂ydt∂zdt∂t rrrr∂V∂V∂V∂V =u+v+w+∂x∂y∂z∂t或 rrrr∂VrdVa==(V.∇)V+ dt∂t或 du∂u∂u∂u∂u=u+v+w+dt∂x∂y∂z∂tdv∂v∂v∂v∂v ay==u+v+w+dt∂x∂y∂z∂tdw∂w∂w∂w∂waz==u+v+w+dt∂x∂y∂z∂tax=The first three term represents convective derivatives and the last one the local derivative. Part Ⅱ Calculation and Analytical Problems 3． 1.52m。正确利用静力学基本方程8分；过程正确5分；答案正确2分 4． (a) 169.4 kPa ; (b) 209 m3/h。正确利用Bernoulli’s方程4; 掌握U型管计算4;掌握连续方程(4);结果正确(3). 5． 3U0bδ。正确利用积分形式质量守恒方程6; 各项简化正确7;结果正确2。 86． （1）是势流或无旋流动。正确写出流函数和速度的关系3；了解判断无旋或有势的条件3；结果正确3。 （2）4800Pa。能利用无旋流动全场Bernoulli’s方程4；结果正确2。 第 页