【正文】 quid. (10 分 ) Solution: )(203555144302232323332111fpsvvgvzpgvzp??????????????)( 2332 fpsA Avv ?????)()/( 0 7 5)1020(552)(22222222323223332222p s iftlbgvvzzpgvzpgvzp????????????????????239)(173)(173)020s in(4)(165)(1654)20c os(4)()(2232332222323323322332??????????????????????????????yxbyybybxxbxyybyyyyxxbxxxxFFFlbFFlbvDvFlbFFlbDpvvDvFvvQFFFFvvQFFFF?????????17. An 180mmdiameter pipeline (f=) 150 m long discharges a 60mmdiameter water jet into the atmosphere at a point that is 80 m below the water surface at intake. The entrance to the pipe is reentrant, with ke=, and the nozzle loss coefficient k2=kn=. Find the flow rate and the pressure at B. (15 分 ) Solution: (a) (b) 18. What minimum value of b is necessary to keep the rectangular stone from sliding if it weighs 160 lb/ft3, a=14ft, c=16ft, and the coefficient of friction is ? With this minimum b value, will it also be safe against overturning? Assume that water dose not get underneath the stone block. (10分 ) Solution1: )/(4.)/()150(80991180602222223211121212212222122212222221212022222000smAvQsmvvvvvDDvvgvgvkgvkgvdlfzzhgvzpgvzpeL????????????????????????????????)(586)()22()22(22)/(522221222222222222212k P aPagvkgvvgvkgvvphgvzpgvzpsmvvBBLBBB???????????????????????)( 2 lbBBBaaAhF cww ????????? ?)(1 1 5 lbbBBbb c BfF sf ??????? ? to keep the rectangular stone from sliding, then Since ∴ it is also safe against overturning. 19. A flow is defined by u=2(1+t), v=3(1+t), w=4(1+t). What is the velocity of flow at the point (3,2,4) at t=2? What is the acceleration at that point at t=2? (10 分 ) Solution: At t=2 20. Water flows over the spillway of constant section. Given that y1 = and y2 = , determine the resultant horizontal force on the spillway per meter of spillway width (perpendicular to the spillway section). Assume ideal flow. (10 分 ) )( 1511 52ftbBbBFF wf???wsswwMftlbBbbc BMftlbBBaFM?????????????).().(?12)21(4)1(49)21(3)1(36)21(2)1(2??????????????????twtvtu432???????????????????????????????????????zwwywvxwutwazvwyvvxvutvazuwyuvxuutuazyx222222222222???????????????zyx aaaawvuVSolution: 將 y1 = , y2 = , p1 = p2 , γ =9810 N/m2 , 代入得 解得： v1 = , v2 = To the right 21. Water and oil in an open storage tank. (a) Find the total forces exerted by the fluids on a tank wall, and (b) the location of the center of pressure. (10 分 ) Solution: (a) (b) gvypgvypyvyv22222221112211????????222121??????vvvv)()/(42960)(2981029810)(22)()(221211221112112112kNFFmNBFvvByvByyByyFvvByvFFFvvQFbbbbxxx????????????????????????????????39。已知管徑 d=50 mm， AB 段長度 LAB = m，流量 qv = 15 m3/h，沿程阻力系數(shù) λ =，兩測壓管中的水柱高度差 Δ h = 20 mm，求彎頭的局部阻力系 數(shù) ξ 。 解：由連續(xù)方程： 得： 選彎管所圍成的體積為控制體，對(duì)控制體列 x 方向動(dòng)量方程： 14. 為測定 90186。彎管轉(zhuǎn)向水平方向流動(dòng)。（ 15 分） 解：設(shè) FD = f (D, v, ρ ,μ ) 選 D、 v、ρ 為基本變量 上述方程的量綱方程為： 由量綱一致性原則，可求得： a1=1 a2=1 b1=2 b2=1 c1=2 c2=1 ∴ 12. 如圖所示，一封閉容器內(nèi)盛有 油和水，油層厚 h1=40 cm，油的密度 ρ o=850 kg/m3，盛有水銀的 U 形測壓管的液面距水面的深度 h2=60 cm，水銀柱的高度低于油面 h=50 cm，水銀的密度 ρ hg= 13600 kg/m3，試求油面上的計(jì)示壓強(qiáng)（ 15 分）。 解：由連續(xù)方程： 由能量方程： X 方向動(dòng)量方程： Y 方向動(dòng)量方程： 合力為 : 11. 小球在不可壓縮粘性流體中運(yùn)動(dòng)的阻力 FD 與小球的直徑 D、等速運(yùn)動(dòng)的速度 v、流體的)(1 5 0 011 5 0 02222Nkkk FFFFkkkklvmppmlvF?????????)/()( 21222121122211smvddAAvvAvAv??????)(21725)(2)(222224222112222211Pavvppgvgpgvgpeeee??????????????)(42 1 7 2 5)010(4 0 0 0)()(2222122212NApvvqFApFvvqexxvxexxxv????????????????????)(4)(4)()(24211121112NApvvqFApFvvqeyyvyeyyyv?????????????????????)( 4 2 3 2 2222 NFFF yx ?????密度 ρ 、動(dòng)力粘度 μ 有關(guān)，試導(dǎo)出阻力的表達(dá)式 。漸縮彎管放在水平面上，管 徑 d1=15 cm， d2= cm，入口處水平均流速 v1= m/s，靜壓 p1e= 104 Pa（計(jì)示壓強(qiáng)）。在該風(fēng)速下測得模型的風(fēng)阻力為 1500N，試求原型在最大行駛速度時(shí)的風(fēng)阻。 解：（ 1）上半球固定在支座上時(shí) （ 2）下半球固定在支座上時(shí) 9. 新設(shè)計(jì)的汽車高 ，最大行駛速度為 108km/h，擬在風(fēng)洞中進(jìn)行模型試驗(yàn)。當(dāng)測壓管讀數(shù) H=3m時(shí)，不計(jì)球的自重，求下列兩種情況下螺栓群 AA 所受的拉力。 （ dimΔ P =ML1T2， dimμ =ML1T1）。模型與實(shí)物的比例尺為 1/3，已知實(shí)際情況下魚雷速度 vp=6 km/h，海水密度ρ p=1200 kg/m3，粘度ν p= 106 m2/s，空氣的密度 ρm= kg/m3，粘度νm= 105 m2/s，試求：（ 1）風(fēng)洞中的模擬速度應(yīng)為多大？（ 2）若在風(fēng)洞中測得模型阻力為 1000N，則實(shí)際阻力為多少？