FLUID MECHANICS Time: 1 hour (ECE-301) Max. Marks :30

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1 B.Tech. [SEM III(ME&CE)] QUIZ TEST-1 (Session : ) Time: 1 hour (ECE-301) Max. Marks :30 Note: Attempt all questions. PART A Q1. The velocity of the fluid filling a hollow cylinder of radius 0.1 m varies as u = 10 [1-(r/0.1) 2 ]m/s along the radius r. The viscosity of the fluid is Ns/m 2. For 2 m length of the cylinder, determine the shear stress and shear force over cylindrical layers of fluid at r =0 (centre line), 0.02, and 0.1 m (wall surface.) (Q.No.6) [2+3=5] Q2. The wall of a reservoir is inclined at 30 to the vertical. A sluice 1m long along the slope and 0.8 m wide is closed by a plate. The top of the opening is 8 m below the water level. Determine the location of the centre of pressure and the total force on the plate. (Q.No.12) [3+2=5] PART B Q1.(a)Define the term Centre Of Buoyancy and Meta-centric Height. [2+2] (b)prove that the total pressure exerted by a static fluid on an inclined plane submerged surface is the same as the force exerted on a vertical plane surface as long as the depth of the centre of gravity of the surface is same. [4] Q2.The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5mm Q3.A body has the cylindrical upper portion of 3 m diameter and 1.8 m deep. The lower portion is a curved one, which displaces a volume of 0.6 m 3 of water. The centre of buoyancy of the curved portion is a at a distance of 1.95 m below the top of the cylinder. The centre of gravity of the whole body is 1.20m below the top of the cylinder. The total displacement of water is N. Find the meta centric height of the body. [7] X ECE-301/Mr. Shivendra Srivastava,Mr. Shiv Pratp Yadav, Mr. Ajay Kumar Date: 02/09/2013 Page-1

2 B.Tech. [SEM III(ME&CE)] QUIZ TEST-1 (Session : ) Time: 1 hour (ECE-301) Max. Marks :30 Note: Attempt all questions. PART A Q1. The space between two large inclined parallel planes is 6mm and is filled with a fluid. The planes are inclined at 30 to the horizontal. A small thin square plate of 100 mm side slides freely down parallel and midway between the inclined planes with a constant velocity of 3 m/s due to its weight of 2N. Determine the viscosity of the fluid. (Q.No.7) Q2.A wooden beam 0.10m*0.10m*2.75m floats on water. When the beam carries a 25 N load at one end, it gets tilted by 2 the loaded end being at the surface. Find the specific weight of wood. (Q.No.11) PART B Q1.(a)Define the term Centre Of Buoyancy and Meta-centric Height. [2+2] (b)prove that the total pressure exerted by a static fluid on an inclined plane submerged surface is the same as the force exerted on a vertical plane surface as long as the depth of the centre of gravity of the surface is same. [4] Q2.The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5mm Q3.A body has the cylindrical upper portion of 3 m diameter and 1.8 m deep. The lower portion is a curved one, which displaces a volume of 0.6 m 3 of water. The centre of buoyancy of the curved portion is a at a distance of 1.95 m below the top of the cylinder. The centre of gravity of the whole body is 1.20m below the top of the cylinder. The total displacement of water is N. Find the meta centric height of the body. [7] X ECE-301/Mr. Shivendra Srivastava,Mr. Shiv Pratp Yadav, Mr. Ajay Kumar Date: 02/09/2013 Page-1

3 B.Tech. [SEM III(ME&CE)] QUIZ TEST-1 (Session : ) Time: 1 hour (ECE-301) Max. Marks :30 Note: Attempt all questions. PART A Q1. An open cylindrical vertical container is filled with water to a height of 30 cm above the bottom and over that an oil of specific gravity 0.82 for another 40 cm. The oil does not mix with water. If the atmospheric pressure at that location is 1 bar, determine the absolute and gauge pressures at the oil water interface and at the bottom of the cylinder. (Q.No.8) [2+3] Q2.A solid cylinder of diameter 4m has a height of 3m.Find the metacentric height of the cylinder when it is floating in water with its axis vertical. The specific gravity of the cylinder is 0.6.State whether the equilibrium is stable or unstable. (Q.No.14) [4+1] PART B Q1. (a)define the term Centre of Buoyancy and Meta-centric Height. [2+2] (b)prove that the total pressure exerted by a static fluid on an inclined plane submerged surface is the same as the force exerted on a vertical plane surface as long as the depth of the centre of gravity of the surface is same. [4] Q2.The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5mm Q3.A body has the cylindrical upper portion of 3 m diameter and 1.8 m deep. The lower portion is a curved one, which displaces a volume of 0.6 m 3 of water. The centre of buoyancy of the curved portion is a at a distance of 1.95 m below the top of the cylinder. The centre of gravity of the whole body is 1.20m below the top of the cylinder. The total displacement of water is N. Find the meta centric height of the body. [7] X ECE-301/Mr. Shivendra Srivastava,Mr. Shiv Pratp Yadav, Mr. Ajay Kumar Date: 02/09/2013 Page-1

4 B.Tech. [SEM III(ME&CE)] QUIZ TEST-1 (Session : ) Time: 1 hour (ECE-301) Max. Marks :30 Note: Attempt all questions. PART A Q1. The right limb of simple U-tube manometer containing mercury is open to the atmosphere while the left limb is connected to a pipe in which a liquid of specific gravity 0.95 is flowing. The centre of the pipe is 0.3 m below the level of mercury in the right limb. Find the pressure of liquid in the pipe if the difference between the levels of mercury in the two limbs is 0.5 m (as shown in fig.) (Q.No.9) Q2. The specific weight of a liquid varies as γ = 9810 (1 + y) where y is measured in m, downward from the surface. A block 1 m 2 m area and 2 m deep weighing N floats in the liquid with the 2 m side vertical. Determine the depth of immersion. (Q.No.15) PART B Q1.(a)Define the term Centre Of Buoyancy and Meta-centric Height. [2+2] (b)prove that the total pressure exerted by a static fluid on an inclined plane submerged surface is the same as the force exerted on a vertical plane surface as long as the depth of the centre of gravity of the surface is same. [4] Q2.The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5mm Q3.A body has the cylindrical upper portion of 3 m diameter and 1.8 m deep. The lower portion is a curved one, which displaces a volume of 0.6 m 3 of water. The centre of buoyancy of the curved portion is a at a distance of 1.95 m below the top of the cylinder. The centre of gravity of the whole body is 1.20m below the top of the cylinder. The total displacement of water is N. Find the meta centric height of the body. [7] X ECE-301/Mr. Shivendra Srivastava,Mr. Shiv Pratp Yadav, Mr. Ajay Kumar Date: 02/09/2013 Page-1

5 B.Tech. [SEM III(ME&CE)] QUIZ TEST-1 (Session : ) Time: 1 hour (ECE-301) Max. Marks :30 Note: Attempt all questions. PART A Q1.A vertical gate closes a horizontal tunnel 5m highh and 3m wide running full with water. The pressure at the bottom of gate is KN/m 2.Determine the total height of water, pressure force on the gate and position of centre of pressure. (Q.No.10) [1+2+2] Q2. A rectangularr plane having 3 m width and 3 m height is submerged vertically in an oil of specific gravity The vertex of the triangular surface is above its base and just touches the free surface of oil. Find: (i) The force acting on the surface due to oil pressure. (ii) The depth of the centre of pressuree from free surface. (Q.No.13) [2+3] PART B Q1.(a) )Define the term Centree Of Buoyancy and Meta-centric Height. [2+2] (b)prove that the total pressure exerted by a static fluid on an inclined plane submerged surface is the same as the force exerted on a vertical plane surface as long as the depth of the centre of gravity of the surface is same. [4] Q2.The dynamic viscosity of an oil, used for lubrication between a shaft and sleeve is 6 poise. The shaft is of diameter 0.4 m and rotates at 190 r.p.m. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5mm Q3.A body has the cylindricall upper portion of 3 m diameter and 1.8 m deep. The lower portion is a curved one, which displaces a volume of 0.6 m 3 of water. The centre of buoyancy of the curved portion is a at a distance of 1.95 m below the top of the cylinder. The centre of gravity of the whole body is 1.20m below the top of the cylinder. The total displacement of water is N. Find the meta-centric height of the body. [7] X

6 QUIZ TEST-2 (Session: ) Time: 1 hour (ECE-301) Max. Marks: 30 Note: All questions are compulsory. Q1) The water is flowing through a taper pipe of length 100m having diameter 600mm at the upper end and 300 mm at lower end, at the rate of 50lit/sec. the pipe has a slope of 1 in 30. Find the pressure at the lower end. If the pressure at the higher level is N/cm 2. Q(2) Q2)The efficiency ή of a fan depends on density ρ, dynamic viscosity of the fluid µ, angular velocity ώ, diameter d of the rotor and discharge Q. Express the efficiency in terms of dimensionless parameters. Q(9) Q1) Derive Euler equation of motion for flow along a stream line and prove that (P/ρg +V 2 /2g+Z) = constant Q2) a) Differentiate between orifice meter and venturimeter. Explain any four dimensionless number and its practical applications in fluid mechanics. [2+2+2] b) A spillway 7.2 m high and 150m long discharges 2150 m 3 /s under a head of 4m. If a 1.16 model of spillway is to be constructed, find [2] i. Head over the model ii. The model discharge Q3) a) Define momentum equation and moment of momentum equation. [2] b) 250 lit/sec of water is flowing in a pipe having diameter of 300 mm. if the pipe is bent by 135 o, find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm 2. X ECE-301 / Mr. Shivendra Srivastava, Mr.Shiv Pratap Yadav, Mr. Ajay Kumar Date: 31 / 10 / 2013

7 QUIZ TEST-2 (Session: ) Time: 1 hour (ECE-301) Max. Marks: 30 Note: All questions are compulsory. Q1) Water is flowing through a pipe having a diameter 300mm and 200mm at the bottom and upper respectively. The intensity of pressure at the bottom and is N/cm 2. And the pressure at upper end is 9.81N/cm 2. Determine the difference in datum head if the rate of flow through pipe is 40lit/sec. (Q1) Q2)The pressure difference Δ p in a pipe of diameter d and length l due to turbulent flow depends on the velocity v, viscosity µ, and density ρ and roughness k. Using Buckingham pie theorem, obtain expression for Δ p. (Q10) Q1) Derive Euler equation of motion for flow along a stream line and prove that (P/ρg +V 2 /2g+Z) = constant Q2) a) Differentiate between orifice meter and venturimeter.explain any four dimensionless number and its practical applications in fluid mechanics. [2+2+2] b) A spillway 7.2 m high and 150m long discharges 2150 m 3 /s under a head of 4m. If a 1.16 model of spillway is to be constructed, find [2] i. Head over the model ii. The model discharge Q3) a) Define momentum equation and moment of momentum equation. [2] b) 250 lit/sec of water is flowing in a pipe having diameter of 300 mm. if the pipe is bent by 135 o, find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm 2. X ECE-301 / Mr. Shivendra Srivastava, Mr.Shiv Pratap Yadav, Mr. Ajay Kumar Date: 31 / 10 / 2013

8 QUIZ TEST-2 (Session: ) Time: 1 hour (ECE-301) Max. Marks: 30 Note: All questions are compulsory. Q1) Find the discharge of water flowing through a pipe 30 cm diameter placed in an inclined position where a venturimeter is inserted, having a throat diameter of 15 cm. The difference of pressure between the main and the throat is measured by a liquid of specific gravity 0.6 in an inverted U-tube which gives a reading of 30cm. The loss of head between the main and the throat is 0.2 times the kinematic head of the pipe. (Q4) Q2) The resisting force R of a supersonic plane during flight can be considered as dependent upon the length of the aircraft L, velocity V, air viscosityµ, density ρ and the bulk modulus K. Express the relationship by using Rayleigh s method. (Q11) Q1) Derive Euler equation of motion for flow along a stream line and prove that (P/ρg +V 2 /2g+Z) = constant Q2) a) Differentiate between orifice meter and venturimeter. Explain any four dimensionless number and its practical applications in fluid mechanics. [2+2+2] b) A spillway 7.2 m high and 150m long discharges 2150 m 3 /s under a head of 4m. If a 1.16 model of spillway is to be constructed, find i. Head over the model ii. The model discharge [2] Q3) a) Define momentum equation and moment of momentum equation. [2] b) 250 lit/sec of water is flowing in a pipe having diameter of 300 mm. if the pipe is bent by 135 o, find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm 2. X ECE-301 / Mr. Shivendra Srivastava, Mr.Shiv Pratap Yadav, Mr. Ajay Kumar Date: 31 / 10 / 2013

9 QUIZ TEST-2 (Session: ) Time: 1 hour (ECE-301) Max. Marks: 30 Note: All questions are compulsory. Q1) An orificemeter with orifice diameter 15 cm is inserted in a pipe of 30 cm diameter. The pressure difference measured by a mercury oil differential manometer on the two side of the orificemeter gives a reading of 50 cm of mercury. Find the rate of flow of oil of specific gravity 0.9 when the coefficient of discharge of the orificemeter=0.64. (Q5) Q2) Find an expression for the drag force on smooth sphere of diameter d, moving with a uniform velocity V in a fluid of density ρ and dynamic viscosityµ. (Q8) Q1) Derive Euler equation of motion for flow along a stream line and prove that (P/ρg +V 2 /2g+Z) = constant Q2) a) Differentiate between orifice meter and venturimeter. Explain any four dimensionless number and its practical applications in fluid mechanics. [2+2+2] b) A spillway 7.2 m high and 150m long discharges 2150 m 3 /s under a head of 4m. If a 1.16 model of spillway is to be constructed, find [2] i. Head over the model ii. The model discharge Q3) a) Define momentum equation and moment of momentum equation. [2] b) 250 lit/sec of water is flowing in a pipe having diameter of 300 mm. if the pipe is bent by 135 o, find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm 2. ECE-301 / Mr. Shivendra Srivastava, Mr.Shiv Pratap Yadav, Mr. Ajay Kumar Date: 31 / 10 / 2013 X

10 QUIZ TEST-2 (Session: ) Time: 1 hour (ECE-301) Max. Marks: 30 Note: All questions are compulsory. Q1) A pitot tube is inserted in a pipe of 300 mm diameter. The static pressure in the pipe is 100 mm of mercury (vacuum). The stagnation pressure at the center of the pipe recorded by the pitot tube is 0.981N/cm 2. Calculate the rate of flow of water through pipe if the mean velocity of flow is 0.85times the central velocity. Take C v =0.98 (Q6) Q2) A horizontal venturimeter with inlet diameter 200mm and throat diameter 100mm is employed to measure the flow of water. The reading of the differential manometer connected to the inlet is 180mm of mercury. If the coefficient of discharge is Find the rate of flow. (Q16) Q1) Deive Euler equation of motion for flow along a stream line and prove that (P/ρg +V 2 /2g+Z) = constant Q2) a) Differentiate between orifice meter and venturimeter. Explain any four dimensionless number and its practical applications in fluid mechanics. [2+2+2] b) A spillway 7.2 m high and 150m long discharges 2150 m 3 /s under a head of 4m. If a 1.16 model of spillway is to be constructed, find [2] i. Head over the model ii. The model discharge Q3) a) Define momentum equation and moment of momentum equation. [2] b) 250 lit/sec of water is flowing in a pipe having diameter of 300 mm. if the pipe is bent by 135 o, find the magnitude and direction of the resultant force on the bend. The pressure of water flowing is 39.24N/cm 2. X ECE-301 / Mr. Shivendra Srivastava, Mr.Shiv Pratap Yadav, Mr. Ajay Kumar Date: 31 / 10 / 2013

SPECIAL QUIZ TEST (Session : 2013-14) Time:1hr (ECE-301) Max. Marks:30 Note: Attempt all questions Q.

11 SPECIAL QUIZ TEST (Session : ) Time:1hr (ECE-301) Max. Marks:30 Note: Attempt all questions Q.1)The right limb of simple U-tube manometer containing mercury is open to the atmosphere while the left limb is connected to a pipe in which a liquid of specific gravity 0.95 is flowing. The centre of the pipe is 0.3 m below the level of mercury in the right limb. Find the pressure of liquid in the pipe if the difference between the levels of mercury in the two limbs is 0.5 m (as shown in fig.) (Q.9) Q2) State the Newton s law of viscosity and derive the equation of viscosity? What is the effect of temperature on viscosity of water and air? (Q.1) (1+2+2) Q.1) Derive an expression for the force exerted on submerged vertical plane surface by the static liquid and locate the position of centre of pressure. Q.2) Define the terms buoyancy and centre of buoyancy. Explain the terms meta-center and Meta-centric height. ( ) Q3) A circular plate of diameter 1.2 m is placed vertically in water in such a way that the center of the plate is 2.5 m below the free surface of water. Determine the total pressure and the position of the center of pressure [3+2] X ECE-301/Mr Shivendra Srivastava,Mr. Shiv Pratap Yadav,Mr Ajay Kumar Date: / / Page-1

12 SPECIAL QUIZ TEST (Session : ) Time:1hr (ECE-301) Max.Marks:30 Note: Attempt all the questions Q1) The space between two large inclined parallel planes is 6mm and is filled with a fluid. The planes are inclined at 30 to the horizontal. A small thin square plate of 100 mm side slides freely down parallel and midway between the inclined planes with a constant velocity of 3 m/s due to its weight of 2N. Determine the viscosity of the fluid. (Q-7) (5) Q2) Derive an expression for the meta-centric height of a floating body. (Q-5) (5) Q.1) Derive an expression for the position of centre of pressure on submerged inclined plane surface. (5) Q.2) Find the volume of the water displaced and position of centre of buoyancy for a wooden block of width 3m and depth 2m, when it floats horizontally in water. The density of wooden block is 700 kg/ms 3 and its length7m. (2+3) Q.3) what do you understand by Total Pressure and Center of Pressure? Discuss the effect of position of meta-centre on the floating body. (1+1+3) X ECE-301/Mr. Shivendra Srivastava,Mr. Shiv Pratap Yadav, Mr. Ajay Kumar Date: / / Page-1

Irrigation &Hydraulics Department lb / ft to kg/lit.

CAIRO UNIVERSITY FLUID MECHANICS Faculty of Engineering nd Year CIVIL ENG. Irrigation &Hydraulics Department 010-011 1. FLUID PROPERTIES 1. Identify the dimensions and units for the following engineering