Hydraulics and Fluid Mechanics Questions

• Venturimeter – Primary Use in Internal Flow Measurement A Venturimeter installed in a pipe is used to determine the volumetric discharge of the liquid flowing through that pipe using pressure differences and Bernoulli’s principle.
• Rectangular Weir with End Contractions – Francis Discharge Formula For a sharp-crested rectangular weir having n end contractions, the practical Francis form in SI units is Q = 1.84 * (L − 0.1 * n * H) * H^(3/2), where L is crest length and H is head over crest.
• Temperature Effect – Dynamic Viscosity of Gases For most common gases, the dynamic viscosity increases as temperature rises due to enhanced molecular momentum transport.
• Newton’s Law of Viscosity – Relationship Between Shear Stress and Shear Rate According to Newton’s law, the shear stress on a fluid layer is directly proportional to the rate of shear strain (velocity gradient), with proportionality constant equal to the dynamic viscosity.
• Applications of Bernoulli’s Equation – Ideal Energy Balance Under appropriate assumptions (steady, incompressible, negligible losses), Bernoulli’s equation underpins the working principles of the Venturimeter, orifice meter, and Pitot tube.
• Pipe Flow Transition – Definition of Higher Critical Velocity In internal pipe flow, the higher critical velocity corresponds to the speed (or Reynolds number) above which turbulence is fully established; hence the statement that turbulent flow starts at the higher critical velocity is correct.
• Surface Tension – Ability of a Liquid Surface to Resist Tension Statement: The property of a liquid that enables its free surface to resist a tensile stress (pulling apart) is called surface tension.
• Most Efficient Rectangular Channel Section – Proportion for Maximum Discharge For a given area and bed slope, a rectangular channel conveys maximum discharge when the breadth is twice the flow depth (b = 2 y), which maximizes hydraulic radius.
• Hemispherical Tank Draining – Time to Lower Level from H1 to H2 A hemispherical tank of radius R drains through a small orifice of area a at its bottom. Including coefficient of discharge Cd, the time to reduce the liquid head from H1 to H2 (measured from the orifice) is t = (pi / (Cd * a * sqrt(2 * g))) * [ (4 * R / 3) * (H1^(3/2) − H2^(3/2)) − (2 / 5) * (H1^(5/2) − H2^(5/2)) ].
• Venturi Flume — Typical Range of Coefficient of Discharge (Cd) For a properly calibrated Venturi flume operating under free-flow (submergence not excessive), the overall coefficient generally lies in which range?
• Internal Mouthpiece — Running Full Criterion An internal (re-entrant) mouthpiece is said to be running full if the length of the mouthpiece exceeds which condition relative to the orifice diameter?
• Terminology — Short Pipe Fitted to an Orifice A pipe whose length is greater than about twice the orifice diameter, fitted externally or internally to the orifice, is termed as:
• Venturi Flume — Pressure Regime During Flow In a Venturi flume operating correctly in an open channel, the water through the throat flows at which pressure condition?
• Nozzle at Pipe End — Nature of Exit Jet A nozzle fitted at the end of a water pipeline primarily delivers water at which condition at the outlet?
• Venturimeter Design — Throat/Pipe Diameter Ratio to Avoid Separation To avoid flow separation at the throat in a Venturimeter, a commonly recommended ratio of throat diameter (d_t) to pipe diameter (D) is approximately:
• Open-Channel Regime — Depth Compared to Critical Depth If the flow depth y in an open channel is less than the critical depth y_c, how is the flow classified?
• Fluid Classification — Definition of Non-Newtonian Fluid State whether the following statement is correct: ‘‘A fluid whose viscosity changes with the rate of deformation (shear rate) is called a non-Newtonian fluid.’’
• Rheology — Fluid Obeying Newton’s Law of Viscosity A fluid that obeys Newton’s law of viscosity (shear stress proportional to shear rate with constant viscosity) is termed a:
• Dam Spillways — Weir Profile Commonly Used Which type of weir profile is most commonly adopted for dam spillways to match the underside of the free overfall (design nappe) and pass large discharges efficiently?
• Critical flow in open channels: At the critical depth (y_c), what happens to the discharge for a given specific energy or channel control condition?