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Note for Fluid Mechanics - FM By Himanshu Chauhan

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Fluid Mechanics 3. Find the viscosity in poise of a liquid through with a steel ball of diameter 1mm falls, with a uniform velocity of 20 mm/s .The specific gravity of the liquid is 0.91 and that of steel is 7.8. Given that k=3ΒΆ 𝑁 𝑃 4. The equation for specific speed for a turbine is given by 𝑁𝑠 = 5ΰ΅— by ΒΆ-theorem 𝐻 4 and using variables such as power p, speed N, head H, diameter D of the turbine, density ρ of the fluid and acceleration due to gravity g, deduce the above expression for 𝑁𝑠 .

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Fluid Mechanics 5. Water at 15Β°C flows at 4 m/s in a 150 mm pipe. At what velocity must oil at 30Β°C flow in a 75 mm pipe for the two flows to be dynamically similar? Take kinematic viscosity for water at 15Β°C as 1.145x10βˆ’6 π‘š2 /s and that for oil at 30Β°C as 3.0x10βˆ’6 π‘š2 /s. Answer: 20.96 π‘š2 /s 6.A model with length scale ratio, model to prototype, equal to x, of a Mach 2 supersonic aircraft is tested in a wind tunnel, wherein air is maintained at atmospheric temperature and a pressure of y times atmospheric pressure. Determine the speed of the model in the tunnel. Given that the velocity of sound in atmospheric air = z. Answer π‘‰π‘š = 2𝑧 π‘₯𝑦

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Fluid Mechanics 7. A solid sphere of diameter 100 mm moves in water at 5m/s . It experiences a drag of magnitude 19.62 N .What would be the velocity of 5m diameter sphere moving in air in order to ensure similarity? What will be the drag experienced by it ? State which law governs the similarity. Take ρ𝑀 =1000kg/π‘š3 ;Οπ‘Žπ‘–π‘Ÿ =1.2kg/π‘š3 ;kinematic viscosity of air = 13kinematic viscosity of water. Answer: 𝐹𝑃 = 872 N 8. A 1:10 scale model of a submarine moving far below the surface of water is tested in a water tunnel. If the speed of the prototype is 8 m/s, determine the corresponding velocity of water in tunnel. Also determine the ratio of the drag for the model and prototype.ρ𝑀 =1000kg/π‘š3 ; Οπ‘ π‘’π‘Ž π‘€π‘Žπ‘‘π‘’π‘Ÿ =1027kg/π‘š3 ¡𝑀 = 0.001 ; Β΅π‘ π‘’π‘Ž π‘€π‘Žπ‘‘π‘’π‘Ÿ =1.151267x10βˆ’3 Answer: 71.365 m/s,0.775

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Fluid Mechanics 9. An overflow structure 550m long is designed to pass a flow of 4400 m3/s. A 1:20 model of the cross-section of the structure is built in a laboratory channel 0.5m wide. Calculate the corresponding flow rate for model if the action of the viscosity and surface tension may be neglected. When the model is tested at this flow rate the pressure at the point on the model is observed to be 50 mm of mercury vacuum, how should this be interpreted. Answer: 0.0447 m3/s 10. In 1 in 40 model of a spillway, the velocity and discharge are 2m/s 2.5m3/s. Find the corresponding velocity and discharge in the prototype. Answer:12.65m/s,25298.2 m3/s.

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