升力线理论用何种模型近似有限翼展机翼的诱导阻力？
What model does Prandtl's lifting-line theory use to approximate induced drag of a finite-span wing?
升力线理论把机翼用一根沿展向绑定环量的涡线表示，并拖出自由涡系形成尾涡面。由毕奥-萨伐尔定律求得下洗，诱导阻力正比于环量沿展向分布的二阶矩，椭圆载荷分布时诱导阻力最小。
Lifting-line theory models the wing as a spanwise bound vortex carrying circulation, trailing a free vortex sheet. Biot-Savart law gives the downwash, and induced drag is proportional to the second moment of the circulation distribution; an elliptic loading minimizes it.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《空气动力学》（国防工业出版社）
Introduction to Flight, Anderson
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787810775090（豆瓣书目条目: 空气动力学）
#升力线理论 #诱导阻力 #尾涡
边界层分离是怎样产生的，它对翼型阻力有什么影响？
How does boundary-layer separation occur, and how does it affect airfoil drag?
当逆压梯度足够大时，边界层内靠近壁面的流体动能被耗尽、出现回流，边界层从壁面脱离形成分离区与尾涡。分离显著增大压差阻力，并可能导致失速。
Under a sufficiently strong adverse pressure gradient, near-wall fluid in the boundary layer loses momentum and reverses, causing the layer to detach and form a separated wake with vortices. Separation sharply increases pressure drag and can trigger stall.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Schlichting & Gersten《Boundary-Layer Theory》（Springer，第8版）
Schlichting & Gersten, Boundary-Layer Theory, Springer
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL11833044W：Boundary-layer theory（
#边界层分离 #逆压梯度 #压差阻力
卡门涡街是如何形成的，它对工程结构有何危害？
How does a Karman vortex street form, and what harm can it cause to engineering structures?
流体绕流钝体时周期性交替脱落的旋涡在下游排成两列，形成卡门涡街。其脱落频率与结构固有频率接近时会诱发涡激振动，长期作用可致桥梁、烟囱等疲劳损伤甚至破坏。
Flow past a bluff body sheds vortices alternately, arranging into two staggered rows downstream known as a Karman vortex street. When the shedding frequency nears a structure's natural frequency it causes vortex-induced vibration, which can fatigue and even destroy bridges or chimneys over time.
难度 专业 · 适合 高中(15-18)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
Blevins《Flow-Induced Vibration》（Van Nostrand Reinhold）
Blevins, Flow-Induced Vibration, Van Nostrand Reinhold
#卡门涡街 #涡激振动 #钝体绕流
伯努利原理如何解释飞机机翼产生升力的现象？
How does Bernoulli's principle explain lift generation on an aircraft wing?
机翼上表面弯曲使气流流速更快，依据伯努利方程动压升高导致静压降低；下表面流速慢、静压较高，上下压差形成向上的升力。实际升力还离不开迎角造成的环量与牛顿第三定律的反作用。
The curved upper surface speeds up airflow, lowering static pressure by Bernoulli's equation, while the slower lower surface keeps higher pressure, and the pressure difference produces upward lift. In practice lift also relies on the angle-of-attack circulation and Newton's third law reaction.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《流体力学》（清华大学出版社）
Fundamentals of Fluid Mechanics, Munson et al.
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL2677306W：Fundamentals of fluid m
#伯努利原理 #升力 #机翼
雷诺数在流体力学中表征什么，它对流动状态有何指示？
What does the Reynolds number represent in fluid mechanics, and what does it indicate about flow state?
雷诺数是惯性力与黏性力的无量纲比值，反映流动受黏性抑制的程度。数值较小趋向层流，较大则易发展为湍流；它是判断管流与绕流状态的关键判据。
The Reynolds number is the dimensionless ratio of inertial to viscous forces, reflecting how much viscosity suppresses disturbances. Low values tend to laminar flow, high values favor turbulence, and it is a key criterion for pipe and external flows.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《流体力学》（清华大学出版社）
Fundamentals of Fluid Mechanics, Munson et al.
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL2677306W：Fundamentals of fluid m
#雷诺数 #层流 #湍流
什么是失速，飞机为何要避免进入失速状态？
What is stall, and why must aircraft avoid entering it?
失速指迎角超过临界值后机翼上表面边界层大面积分离、升力骤降而阻力剧增的状态。此时操控效率下降、高度迅速损失，若不及时改出可能失控，因此必须避免。
Stall occurs when the angle of attack exceeds a critical value, the upper-surface boundary layer separates massively, lift drops sharply and drag surges. Control effectiveness falls and altitude is lost rapidly, so it must be avoided or corrected promptly.
难度 进阶 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-11-02
来源 · Source
《空气动力学》（国防工业出版社）
Introduction to Flight, Anderson
独立核验依据 · Independent verification: 核验依据 1 ISBN 9787810775090（豆瓣书目条目: 空气动力学）
#失速 #迎角 #边界层分离
文丘里管测量流量的原理是什么，为何比孔板更省能？
What is the principle of a Venturi meter for flow measurement, and why is it more energy-efficient than an orifice plate?
文丘里管依据连续性方程与伯努利方程，在渐缩段加速、喉部取压差推算流量。其流道平缓、无锐边，流动分离与湍流损失小，永久压损远低于突然收缩的孔板。
A Venturi meter applies continuity and Bernoulli: the throat accelerates flow and the pressure drop infers flow rate. Its smooth converging-diverging profile causes little separation or turbulence loss, so permanent pressure loss is far lower than a sharp-edged orifice plate.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录仅给书名，无版次与年份；同一书名常对应多个版次，不臆测具体版本。
ASME MFC-7M《Measurement of Gas Flow by Means of Venturi Tubes》
ASME MFC-7M Measurement of Gas Flow by Means of Venturi Tubes
#文丘里管 #流量测量 #压损
汽车流线型设计降低风阻的主要空气动力学依据是什么？
What aerodynamic rationale underlies using streamlined car shapes to reduce drag?
流线型通过平滑的曲面减缓车身后部逆压梯度，推迟边界层分离、缩小尾流区，从而显著降低压差阻力。风阻系数越低，高速行驶时的油耗与噪声越小。
A streamlined body eases the rear adverse pressure gradient, delays boundary-layer separation, and shrinks the wake, sharply cutting pressure drag. A lower drag coefficient reduces fuel use and noise at high speed.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-04
来源 · Source
Hucho《Aerodynamics of Road Vehicles》（Butterworth-Heinemann，SAE 推荐书目）
Hucho, Aerodynamics of Road Vehicles, Butterworth-Heinemann
独立核验依据 · Independent verification: 核验依据 1 ISBN 9781483102078 (2013)
#流线型 #风阻系数 #压差阻力
离心泵叶轮设计中，比转速ns如何决定叶片出口角和流道形状的选择？低比转速和高比转速泵在性能曲线形状上有何系统性差异？
In centrifugal pump impeller design, how does specific speed ns govern the choice of blade exit angle and flow-passage shape? What systematic differences appear in performance-curve shape between low-ns and high-ns pumps?
比转速综合了流量、扬程与转速，是叶轮几何选型的首要无量纲参数：低ns泵采用窄长流道、径向出口和大出口安放角（约60°–90°），高ns泵则流道宽短、出口角减小并逐渐过渡为混流乃至轴流。性能曲线上，低ns泵扬程-流量曲线平坦且关死点扬程高，但高效区窄、易受汽蚀影响；高ns泵曲线陡降，功率曲线随流量上升平缓甚至下降，有利于电机匹配。设计时还须按ns估算效率（如Stepanoff经验式）以避免不切实际的指标。
Specific speed condenses flow rate, head, and shaft speed into the primary dimensionless parameter for impeller selection: low-ns pumps use narrow, long radial passages with large blade exit angles (~60°–90°), while high-ns pumps have wide, short passages with smaller exit angles, transitioning toward mixed-flow and axial designs. On performance curves, low-ns pumps show a flat head-flow curve with high shutoff head but a narrow best-efficiency region and greater cavitation sensitivity; high-ns pumps exhibit steeply falling head curves and power curves that flatten or drop with flow, easing motor sizing. Designers also estimate efficiency from ns correlations (e.g., Stepanoff) to keep targets realistic.
难度 进阶 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-11-03
来源 · Source
Stepanoff,《Centrifugal and Axial Flow Pumps》(Wiley, 1957)；Gülich,《Centrifugal Pumps》第4版(Springer) 第3章
A.J. Stepanoff, Centrifugal and Axial Flow Pumps (Wiley, 1957); J.F. Gülich, Centrifugal Pumps, 4th ed. (Springer), Ch.3
独立核验依据 · Independent verification: 核验依据 1 OPENLIBRARY 标识 /works/OL19833687W：Centrifugal Pumps（首版 2
#泵与叶轮机械 #比转速与叶轮选型
离心泵汽蚀发生时扬程流量曲线为什么会骤然跌落,汽蚀比转速如何衡量泵对汽蚀的敏感程度?
Why does the head-flow curve of a centrifugal pump collapse abruptly once cavitation sets in, and how does suction specific speed gauge its susceptibility?
进口静压降到饱和蒸汽压以下后,叶片前缘大量析出汽泡,汽泡进入高压区溃灭令流道有效过流面积锐减,扬程与效率随之陡降,H-Q曲线呈断裂状。按Gülich的定义,汽蚀比转速Nss=n·Q^0.5/NPSHr^0.75(Q取m³/s)把转速、流量与必需汽蚀余量合成单一指标,常规清水离心泵约在150–250。Nss偏高说明叶轮入口负荷过重,可通过扩大吸入口径、降低转速或加装诱导轮加以缓解。
Once inlet static pressure drops below vapor pressure, copious vapor bubbles form at the blade leading edge; collapsing in the high-pressure region they slash the effective flow area, dropping head and efficiency so steeply that the H-Q curve visibly breaks. Following Gülich's definition, suction specific speed Nss=n·Q^0.5/NPSHr^0.75 (Q in m³/s) folds speed, flow and required NPSH into a single figure of merit, about 150–250 for conventional clean-water pumps. A high value signals overloaded eye geometry, mitigated by enlarging the suction bore, lowering speed, or fitting an inducer.
难度 进阶 · 适合 大众
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：著录含书名，但缺版次 / 出版社 / 年份中的一部分，需编辑补全后才能做独立比对。
Gülich《Centrifugal Pumps》第4版第6章
Gülich, Centrifugal Pumps, 4th ed., Chapter 6, Springer
#汽蚀 #汽蚀比转速