Fluids Questions and Answers

A wooden cube density of wood of side l floats in a liquid of density p with its upper and lower surfaces horizontal If the cube is pushed slightly down and released it performs simple harmonic motion of period T Then T is equal to O 2T O 2T 2T 36 2g l 3g 3 g 4

The pressure of water in a water pipe when tap is opened and closed is respectively 3 105 N m and 3 5 x 105 N m With open tap the velocity of water flowing is 1 10 m s 2 5 m s 3 20 m s 4 15 m s

Two soap bubbles of different radii are connected by a tube then Air flows from bigger bubble to smaller bubble till their size becomes equal Air flows from smaller to larger bubble till their size are interchanged There is no flow of air Air flows from smaller bubble to larger bubble

9 Two vessels A and B have the same base area ar contain water to the same height but the mass water in A is four times that in B The ratio of th liquid thrust at the base of A to that at the base of is l 1 4 1 3 1 1 A A l 2 2 1 4 16 1 B

Two co axial glass tubes forming an annulus with small gap are immersed in clean water The inner and outer radii of the annulus are r and ro respectively What is the capillary rise of water in the annulus if o is the surface tension of water is constant with air p is the density of water and g acceleration due to gravity a b c 20 pg ro r 40 pg ro ri d 80 pg ro r O pg ro r

A capillary tube is dipped in a liquid such that the height to which liquid is raised is 40 cm The capillary tube is inclined at an angle 37 with vertical The length upto which the liquid rises in tube is 15 cm 20 cm 45 cm 50 cm

The area of the inner cross section of a horizontal tube fixed is A while the area of cross section of its part on the right hand side is KA where K two parts are attached smoothly without any sharp turns as given In the tube there is some liquid that can be pushed out of this part of tube The which leaves the tube hits a vertical wall and spreads out creating a tapering film of fluid A At what constant speed does the piston moves if external force has constant value F 2 F O 5 K KA 0 22 K 2 F

The surface tension of water at 20 C is 75 x 10 3 N m The difference in the water surfaces within and outside an open ended capillary tube of 1 mm internal bore inserted at the water surface would nearly be b 10 mm d 20 mm a 5 mm c 15 mm

given below the lists List l A Newtonian fluid B Ideal fluid C Thixotropic fluid D Rheological fluid List II 1 Frictionless and incompressible 2 Viscosity is invariant with shear stress 3 Viscosity increases at higher shear stress 4 Viscosity decreases at higher shear stress Codes A 2 4 1 1 4 B C D 3 2 a b 3

The velocity distribution for flow over a plate is given by u 0 5y y2 where u is the velocity in m s at a distance y meter above the plate If the dynamic viscosity of the fluid is 0 9 N s m then what is the shear stress at 0 20 m from the boundary a 0 9 N m c 2 25 N m b 1 8 N m d 0 09 N m

The density of of aluminum is 2700 kg m The density of gold is 1 93 x 104 kg m of gold What volume of aluminum will have the same mass as 0 500 m 07 15 m 9650 m 3 57 m 1350 m 0 280 m

The velocity of a small ball of mass M and density d when dropped in a container filled with glycerine becomes constant after some time If the density of glycerine is d the viscous force acting on the ball will be

A liquid is under streamline flow through a horizontal pipe of non uniform cross sectional area If the volume rat of flow at a cross section of area a is V then volume rate of flow at a different cross section of area O 2 2V V

V0 3R 43 A cylindrical drum open at the top contains 15 litres of water It drains out through a small opening at the bottom 5 litres of water comes out in time the next 5 litres in further time and the last 5 litres in further time Then c 1 1 1 b 1 1 d 1 1

is flowing out from the full tank with a hole near bottom If area of container is 10 times the area of hole then time level to get lowered from the height of 81 cm to 49 cm is 2 5 7 3 S S

A large tank of area A contains liquid of density A cylinder of density 4 and length and area a a A is kept in equilibrium by applying an external vertically downward force The cylinder is just submerged in liquid Atr 0 the external force disappears instantaneously Answer the following questions The maximum height attained by centre of mass of cylinder from the liquid surface A 3 B 3 C D

Water is flowing out from the full tank with a hole near bottom If area of container is 10 times the area of hole then time taken by water level to get lowered from the height of 81 cm to 49 cm is 0v2 03 V55

Consider a triangular plate as shown in Fig Air flows over on its both sides with an approach velocity of 2 m s Take air p 1 205kg m v 15 06 x 10 m s Determine the shear force on both sides of the plate 2m s 45 Plate L 1 m

A Prandtl tube Pitot static tube with C 1 is used to measure the velocity of water The differential manometer reading is 10 mm of liquid column with a relative density of 10 Assuming g 9 8 m s2 the velocity of water in m s is

A jet of water issues from a Nozzle with a velocity 20 m s and it impinges normally on a flat plate moving away from it at 10 m s The cross sectional area of the jet is 0 01 m and the density of water 1000 kg m The force developed on the plate is V 20 m s a 1000 N c 10 N u 10 m s b 100 N d 2000 N

PASSAGE 1 A cylinder of radius R and length L is kept embedded along the wall of a dam such that a flexible to rotate about the hinge as shown Take density of water as p Side view is shown in the figure Neglecting atmospheric pressure 19 20 R The force exerted by water on the cylinder is A pR Lg vertically B vertically D 2R pgl horizontally 2pR Lg 3 C 4R pgl horizontally The net torque exerted by liquid on the cylinder is B clockwise A PASSAGE 2 p R Lg 2 hinge C anticlockwise D 0

163 From the given diagram the speed with which water leaves the tube B of small diameter is 1 2gh 2 2h 2 3 2g h h 4 2g h h A 30 1 B

Three liquids of densities d 2d and 3d are mixed in equal 151 proportions of weights The relative density of the mixture is 1 2 3 11d T 18d 11 13d 9 23d If are 1 2 3 4 152 Th

LA spherical soap bubble of radius 1 cm is formed inside another soap bubble of radius 3 cm The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble as a 0 75 cm 7 5 cm b 0 75 m d 7 5 m

An aeroplane of mass 3 x 104 kg and total wing area of 120 m is in a evel flight at some height The difference in pressure between the upper and lower surfaces of its wings in kilo pascal is g 10 m s 025 05 0 O 10 0 12 5

376 22 A block of wood weighs 12 kg and has a relative density 0 6 It is to be in water with 0 9 of its volume immersed What weight of a metal is needed if the metal is on the top of wood Relative density of metal 14 a 2 kg c 6 kg b 4 kg d 8 kg 23 The mean distance between the atoms of iron is force constant for iron is 28 a c A ste The value a c 29 The di

The radius of a soap bubble is increased from cm to NLE 15 cm If the surface tension of water is 30 dynes per cm then the work done will be 1 180 ergs 2 360 ergs 3 720 ergs 4 960 ergs

what force must a prey whithstand In example 11 1 we calculated the mass of water in a large tank Now we will consider the pressure and force acting on the water retention dam see figure the dam it is 500 m wide and the water is 80 0 m deep at the dam a What is the pressure average over the dam due to water b Calculate the force exerted against the dam F PA P hpg

vii A horizontal oriented tube AB of length rotates with a constant angular velocity about a stationary vertical axis 00 passing though the end A figure 7 63 The tube is filled with an ideal fluid The end 4 of the tube is open the closed end B ha a very small orifice Find the velocity of the fluid relative to th tube as a function of the column height h o h h 0 1 G O 1 1 K 1 Figure 7 63 B 4

ix The fresh water behind a reservoir dam is 15 m deep A horizontal pipe 4 0 cm in diameter passes through the dam 6 0 m below the water surface as shown in figure 7 65 A plug secures the pipe opening a Find the minimum friction force between the plug and pipe wall to that plug does not eject out b The plug is removed What volume of water flows out of the pipe in 3 0 hour Take g 10 m s 15m a 75 36 N b 148 59 m 6m Figure 7 65

tube in which a liquid of acceleration the tube is liquid will fall out of the v A rough surfaced metal cube of size 4 cm and mass 100 gm is placed in an empty vessel Now water is filled in the vessel so that the cube is just immersed in the water Find the average pressure on the bottom surface of vessel which is in contact with the cube Take g 10 m s 1 00625 10 Pa

In a horizontal pipe line the pressure falls by 16 Nm between two points separated by a distance of 2 km Density of oil is 800 kg m 3 Change in kinetic energy per kg of the oil flowing in the tube is 1 2 x 10 J kg 2 2 10 J kg 3 2 x 10 J kg 4 2 x 10 J kg

r ii A siphon has a uniform circular base of diameter with its crest A 1 8 m above water level as in figure 7 61 Find a velocity of flow b discharge rate of the flow in m sec c absolute pressure at the crest level A Use Po 105 N m s g 10m s 1 8m a 6 2 m s h 96 5 A Figure 7 61 Y 10 3 m3 3 6m cm W gaiv tors sen 2160 m

i A rubber ball of mass 10 gm and volume 15 cm is dipped in water to a depth of 10m Assuming density of water uniform throughout the depth if it is released from rest Find take g 9 8 m s a the acceleration of the ball and b the time taken by it to reach the surface 4 9m s2 2 02s

The velocity of flow of a liquid through an orifice at the bottom of a tank depends on the A Density of the liquid B Area of the cross section of the orifice C Height of the liquid above the orifice D Acceleration due to gravity

2 Two vessels A and B of different shapes have the same base area and are filled with water up to the height h see figure The force exerted by water on the base is FA for vessel A and FR for vessel B The respective weights of the water filled in vessels are WA and WB Then same h A B a FA FBWA WB6 FA FBWA WB C FA FBWA WB d FA FB WA WB

14 Water filled into a container with hexagonal cross section of side 3 tension of water is 0 02 N m then the surface energy of water will be xx 10 J then the value of xis cmsurface SECTION III COMPREHEN SIN TYPE his section contains 2 Paragraphs Based on each paragraph there are 2 questions Each question has 4 options A B C and D for its answer out of which ONLY ONE option can be correct Marking scheme 3 for correct answer 0 if not attempted and 1 in all other cases Paragraph for Question Nos 15 to 16 A circular hole of radius r at the bottom of an initially full water container is sealed by a ball of mass mand radius R R r The depth of the water is now slowly reducedo is the density of the water and V is the volume of the ball inside water

depth and of coefficient of viscosity n The density of the solid is greater than of t liquid The time taken by the body to attain the 90 of the steady state velocity is dependent on A density of the liquid C diameter of the sphere B density of solid D coefficient of viscosity

MULTIPLE CORRECT ANSWER TYPE This section contains 6 multiple choice questions Each question has 4 options A B C and D for its answer out of which ONE OR MORE than ONE option can be correct Marking scheme 4 for all correct options 1 partial marks 0 if not attempted and 2 in all wrong cases A wall of length 1 supports water to a height H as shown in the fig Choose the correct statement s 1 H A The force exerted by water on the wall per unit length is pg B The force exerted by water on the wall is pgH 1 1 C The point of application of the resultant force acts 2H 3 below the free surface D The point of application of the resultant force acts H 3 below the free surface

A cylindrical vessel of area of cross section A and filled with liquid to a height hi has a capillary tube of length 1 and radius r protruding horizontally at its bottom If the viscosity of liquid is n density p and g 9 8 m s the time in which the level of water falls to he is lAInwhere k is pg h A spherical ball of radius 1 104 mand density 104 kg m falls freely under gravity through a distance h before entering a tank of water If after entering the water the velocity of the ball does not change the value of his m the viscosity of water is 9 8 106 Ns m A sphere of radius 0 1m and mass 8 kg is attached to the lower end of a steel wire of length 5m and diameter 10 m The wire is suspended from 5 22m high ceiling of the room When the sphere is made to swing as a simple pendulum it just grazes the floor at its lowest point The velocity of the sphere at the lowest position is

7 4 A tube in vertical plane is shown in figure 7 73 It is filled with a liquid of density p and its end B is closed Then the force exerted by the fluid on the tube at end B will be Neglect atmospheric pressure and assume the radius of the tube to be negligible in comparison to 27 A Patm 40 C P atm 2pgl Ao Figure 7 73 cross section area A Patm pgl Ao D P 4pgl Ao atm the two height A A C

23 An engine pumps water continuously through a hose Water leaves the hose with a velocity u and m is the mass per unit length of the water jet What is the rate at which kinetic energy is imparted to water CBSE AIPMT 2009 a a mu 2 3 b mv c mv 2 2 d m v

D the strains produced in the rods are in the ratio 1 2 3 4 SECTIO N II NUMERICAL VALUE TYPE section contains 8 questions Each question is numerical value For each question enter the correct erical value in decimal notation truncated rounded off to second decimal place 6 25 7 00 0 33 30 30 27 127 30 king scheme 3 for correct answer 0 if not attempted and 0 in all other cases A cylindrical vessel of area of cross section A and filled with liquid to a height has a capillary tube of length 1 and radius r protruding horizontally at its bottom the viscosity of liquid is n density p and g 9 8 m s the time in which the level water falls to ho is In where k is

27 equal small water drops combine to form a big drop if surface tension of water is T and radius of small drop is r then A excess pressure inside big drop is three times of excess pressure inside small drop B surface energy decreases in this process C in this process 72 r T energy releases D radius of big drop is 3r The true statement is Question Type Single Correct Type 1 A B C 2 A B D 3 B C D

Consider two identical cylinders each of mass m density Po horizontal cross section area s in equilibrium partially submerged in two containers filled with liquids of densities P1 and P2 as shown in figure Find the period of small oscillations of this system about its equilibrium neglect the changes in the level of liquids in the containers Neglect mass of the strings acceleration due to gravity is g v is volume of each block

force 7 18 A fixed container of height H with large cross sectional area A is completely filled with water Two small orifice of cross sectional area a are made one at the bottom and the other on the vertical side of the container at a distance H 2 body from the top of the container Find the time taken by the water level to reach a height of H 2 from the bottom of the container H 2 1 g erned m is ody 1 A 24 2H 3a g 3A C 34 2 1 2a H o B D 24 3a 3A 2H 2a g

View in English spheres of volume 250 cc each but of specific gravities 0 8 and 1 2 are connected by string and the combination is immersed in water at equilibrium The tension in the string will be g

A float of cubical shape has sides of 10 cm The float value just touches the valve seat to have a flow area of 0 5 cm as shown in the given figure If the pressure of water in the pipeline is 1 bar the rise of water level h in the tank to just stop the water flow will be a 7 5 cm Float Tank Valve AS b 5 0 cm

A Francis turbine is coupled to an alternator to generate electricity with a frequency of 50 Hz If the alternator has 12 poles then the turbine should be regulated to run at which one of the following constant speeds b 500 rpm d 1000 rpm a 250 rpm c 600 rpm

The point in the immersed body through which the resultant pressure of the liquid may be taken to act is known as kallad f s de foc folur alone and atunci cand chief and a fall th