Fluids Questions and Answers

7 14 A tube with both ends open floats vertically in water Oil with a density 800 kg m is poured into the tube The tube is filled with oil upto the top end in equilibrium state The portion out of the water is of length 10 cm Find the length of oil column Oil 10 cm Water A C S 50 cm 90 cm Figure 7 81 10 cm B 60 cm D 100 cm Oil

7 8 The velocity of the liquid coming out of a small hole of a large vessel containing two different liquids of densities 2p and p as shown in figure 7 76 is A 6gh B gh C 2 2gh D gh 2h 2p Figure 7 76

A small ball is falling in a stationary liquid with a constant speed of 9 m s If we had a ball whose radius is 2 3 times the radius of the original ball what would be the terminal speed in m s of the ball

Q 110 A water drop of almost spherical shape falls in air with uniform velocity Find the difference between radii of curvature at the upper and lower point of drop separated by h 2 3mm T 0 07 N m

A soap bubble of radius R is blown from a soap solution After heating the solution a second bubble of radius 2R is blown The work required to blow the second bubble in comparison to that required for the first bubble is 1 Double 2 Slightly less than double 3 Slightly less than four times 4 Slightly more than four times

A small heavy metallic sphere of specific gravity 2 is suspended by a light inextensible string has period of oscillation T Now it is immersed in water as shown in figure Its period of oscillation now is neglect viscosity A T 2 B 2T C T 2 D T 2 H

A velocity flow field is u x y and v 2x2y determine the stream function and potential function

A velocity flow field is u x y and v 2x2y2 determine the stream function and potential function

Water supplied through a 0 6 m diameter 1000 m long cast iron pipe from an 80 m overhead tank to a village Find the discharge at the village ground level ignoring minor losses due to bends

Air streams horizontally past a small airplane s wings such that the speed is 58 0 m s over the top surface and 48 0 m s past the bottom surface Air streams horizontally past a small airplane s wings such that the speed is 58 0 m s over the top surface and 48 0 m s past the bottom surface What is the direction of the net vertical force including the effects of gravity on the airplane What is the direction of the net vertical force including the effects of gravity on the airplane

A cubical block of mass M floats in a liquid of variable density Py Po 1 2y where y is the depth from the upper surface of the liquid at any instant Initially 1 4 th of the block is immersed If M is the mass of the additional block kept on the first block to just immerse the first block completely then po is a positive constant side of cube 2 units M3M OM 7M M Po 3 On M

A wide container filled with water is suspended with the help of a light spring of stiffness 1000 N m a light inextensible cord and an idea pulley Initially when the system is in equilibrium the plug inserted in an orifice at the centre of the bottom of the container is pulled out The extension in the spring is recorded and shown in the adjoining graph Find the time rate of flow of water from the orifice eeeeeeeeeeeeeeee x cm 4 3 0 2 0 1 0 0 0 10 20 30 t min

quid of density p is flowing through a hole of cross sectional area cross sectional area of vessel If force F which is needed to keep vessel 10 NpgHA then find the value of N 99 st at the instant shown in diagram is Ao F smooth Ao 10 Liquid

3 A slit is cut along the right bottom edge of a rectangular tank The slit is closed by a wooden wedge of mass m and apex angle as shown in the figure The vertical plane surface of the wedge is in contact with the right vertical wall of the tank Coefficient of static friction between these surfaces in contact is u To what maximum height can water be filled in the tank without any leakage through the slit The width of tank is b and density of water is p 2m a pb tan 0 c 2m pb sin 0 cos b d 4m pb tan 0 2m cos pb tan 0 ucose h

Consider a vessel containing homogeneous liquid Two points A and B are taken inside the liquid as shown If PA PB are pressure at points A and E respectively then choose the correct options A Value of PA PB will increase if vessel start accelerating along direction B Value of PA Pg will decrease if vessel is accelerated along y axis C Value of PA Pg will remains unchanged if vessel is accelerated in direction perpendicular to line AB D Value of P P does not depend upon acceleration of the vessel

Vessel shown in the figure has two sections of areas of cross section A and A A liquid of density p fills both sections up to a height h in each Neglect atmospheric pressure A h www h X A A The pressure at the base of the vessel is 2hpg B The force exerted by the liquid on the base is 2hpA g C The weight of the liquid is less than 2hgpA D Ceiling of the vessel at the level x exert a downward force hgp A A on the liquid

Consider a small soap bubble inside a large container having soap solution It orce due to 1st half of soap bubble on IInd half due to surface tension is NRT hen find the value of N 3 14 R radius of bubble T R Soap bubble I II

7 4 A glass tube of radius 0 8 cm floats vertical in water as shown in figure 7 100 What mass of lead pellets would cause the tube to sink a further 3 cm

A copper ball of density 8 6 g cm 3 diameter 1 cm is immersed in oil of density 0 8 g cm If the ball remains suspended in oil in a uniform electric field of intensity 36000 NC 1 acting in upward direction what is the charge on the ball

The horizontal part of the U shaped tube shown in the figure 10 cm and its vertical branches are long enough The cross section of the tube is 1 cm First 20 cm3 water is poured into the tube then 20 cm oil is poured into the left branch density of water 1000 kg m density of oil 800 kg m The whole system is accelerated towards the left at an acceleration of a 10 m sec Determine the difference between the level of water and the level of oil in cm a 10m sec2 10cm

Ans 25113 6 N m 3 A U tube differential manometer connects two pressure pipes A and B Pipe A contains carbon tetrachloride having a specific gravity 1 594 under a pressure of 11 772 N cm and pipe B contains oil of sp gr 0 8 under a pressure of 11 772 N cm The pipe A lies 2 5 m above pipe B Find the difference of pressure measured by mercury as fluid filling U tube Ans 31 36 cm of mercury A differential manometer is connected at the two points A and B as shown in Fig 2 25 At Rair pressure

A string is stretched by a block going over a pulley The horizontal string vibrates in fifth harmonic in unison with a particular tuning fork When a beaker containing a liquid of density p is brought under the block so that it is completely immersed into the liquid the string vibrates in its seventh harmonic in unison with the tuning fork The density of the block is 1 3 24 23 P 49 m 2 49 24 p 14 4 P

A liquid drop of radius 5R is kept in the open atmosphere of pressure Po C is the centre of the liquid drop Two air bubbles are formed inside the liquid drop centred at A and B of radii 2R and R respectively Let the gauge pressure at A B and C are PA PAPB is equal to 32 Find the value of P PB and Pc respectively The ratio of d A BR B

When water freezes into ice its volume increases by 2 A rigid spherical shell is filled completely with water at 0 C Now water is freezed completely then Bulk stress on surface of ice is N X 10 Pa Find the value of N Bulk s modulus of water 2 X 10 1 N m

For an aircraft to travel above Mach 1 work out the velocity required both at sea level and at a cruise altitude of 10 000m with y 1 4 and R 287J kgk LJ

The excess pressure inside a soap bubble of radius 10mm is balanced by a liquid column of 0 04 cm Determine the density of liquid surface tension of soap bubble is 0 03 Nm and g 10m s Options 1 V 2 3 3 10 kg m 4 10 kg m 6 10 kg m 3 3 8 10 kg m

A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground The distance x from the ground where a small hole is punched to get the maximum range R is 2H H X

Max Mark s 01 Multiple Choice Select 1 out of 4 options for the question below As shown following three figures three blocks of different densities 2 and 3 are dropped in a same liquid of density d Then which one relation is correct for following three figures respectively ptions i Ood od and and d ii iii

A Venturi tube is used to measure the speed of a vertically ascending submarine At a given instant the mercury difference in the U shaped arm is h Determine the speed of the submarine with respect to the water I P L water dz L g Pmercu

Suppose that a 15m s wind is blowing across the roof of your house The den sity of air is 1 29 kg m a determine the reduction in pressure that accompanies this wind b explain why some roofs are blown outward during high winds

17 Two rectangular glass slabs of length I and width b are stuck to each other with a liquid film of surface tension T in between them as shown in the figure Find the external force needed to keep them separated in the shown position given the radius of curvature of the liquid surface is R F 1

0 In a hypothetical situation if the viscous force acting on a spherical object of radius r is given as F Av where v is the velocity of the ball and is constant for the fluid If a spherical ball of density 3p is gently released in a fluid of density p from rest Find the terminal velocity of the ball a v R 8png 3A d v R Bpng 54 b v 16pmg 3A 1 8png 3A c v R

A thin capillary of radius 0 1mm is dipped in a liquid with density 1000 kg m surface tension 0 03N m and contact angle 60 If the atmospheric pressure is 105 Pa find a The height H of liquid in the capillary b Radius of curvature of the meniscus c If the length of capillary is H 2 will the liquid flow out If not find the radius of curvature of the meniscus in this case i 0 03m 0 2mm no 0 4mm iii 0 03m 0 2mm yes 0 2mm ii 0 015m 0 1mm no 0 2mm iv 0 0 15m 0 1mm yes 0 2mm

9 A liquid drop of radius 2 cm is just about to fall off the mouth of a tap of radius 2 mm If the density of the liquid is 1000 kg m find the surface tension N m of water a 800 3 b 400 3 c 1000 3 d 200 3

4 A viscous fluid is flowing in a pipe maintained under some pressure difference If the radius and length of the pipe is doubled by what factor should the pressure difference across the tube be changed to maintain the same volume flow rate a 8 b 1 8 c 16 d 1 16

The volume flow rate of a liquid through a pipe of radius r and length l is Q under a pressure head of P then find the volume flow rate through a pipe of quarter the radius and same length under the same pressure head b Q 64 c Q 256 d 256Q a 64Q

Mark the correct statement s about reynold s number a It is the ratio of inertial force of the fluid to the viscous force offered by the fluid b Increases with increase in density and viscosity of fluid c Increases with increase in the diameter of the pipe carrying the fluid d Decreases with increase in viscosity of the fluid e For Reynolds number more than 1000 the flow must be turbulent i a b c d ii a b c d e iii a c d iv a c d e

A wire frame in the shape of circle of radius 2 cm is dipped in soap solution and taken out so that a film is formed If the tension developed in the ring is n x 10 4 N Find the value of n Surface tension of soap solution is 0 03 N m 1 12 2 14 191 19 AF

If the volume flow rate through the pipe AB is Q find the volume flow rate through pipe CD The radius of CD and EF are in ratio 2 1 and their lengths are in ratio 1 1 assume vertical columns to be of negligible length d Q 17 E b 770 F d Q

0 A piece of wood has dimension axbxc It is floating in a liquid of density p such that side a is vertical It is now pushed down gently and released The time period is a 2n palg c 2n g pa b 2n Jabc g d 2n bc pg

Q4 A hole is made on the wall of the cylindrical vessel containing a liquid upto a height h Water is coming out through the hole and falls at a distance r from the base of the cylinder I is found to be maximum when hole is created at depth of 2xh Find the value of x

Consider a situation in which there is a Newtonian fluid between two long coaxial uniformly moving cylinders of radius R and 2R A Force per unit length required to keep the inner cylinder moving is v 6nvo B Force per unit length required to keep the inner cylinder moving is n2 C Distance of the point from the axis at which speed of fluid is zero is 21 3R D Distance of the point from the axis at which speed of fluid is zero is 2R 2v Newtonian fluid between cylinders

6 Read the following passage and answer the questions given below In fluid mechanics Pascal s law plays a very important role to explain the variation of pressure across the liquid Pascal s law states that the pressure in a fluid at rest is the same at all points which are at the same height A change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of the containing vessel Also hydraulic lift has a large cross section and a small cross section filled with liquid having equal pressure at equal heights at both cross sections a On which principle does the hydraulic lift works b A hydraulic lift has a large cross section and a small cross section Large cross sectional area is 10 times the small cross sectional area If the small cross section is given an input force of 10 N then determine the force acting at the large cross sectional area 3 c In a completely filled water tank at rest there are two imaginary points A and B at height 1 cm and 2 cm from the bottom respectively At which point the liquid pressure is more

2 A cylindrical water tank of 10 m depth is completely filled with water Find the velocity of the efflux of water through a small hole on the side wall of the cylinder near its bottom Take g 10 m s 2

45 An open pipe of sufficient length is dipping in water with a speed v vertically If at any instant I is length of tube above water then the rate at which fundamental frequency of pipe changes is speed of sound c CV B 41 A 2v cl C C 2 2 D C 4v 1

A wire is bend at an angle 0 A rod of mass m can slide along the bend wire without friction as shown in figure If a soap film is maintained in the frame and frame is kept in a vertical position the rod is in equilibrium 0 90 m 100 g l 1 m IA can m rod of mass m Surface tension of the soap solution is in S I systeml

A ball of mass m is dropped from a great height After it has fallen through 50 m it attains its terminal velocity and continues to fall The work done against air friction in the first 50 m fall is O equal to the weight mg O greater than the weight mg greater than the work done during second 50 m fall O less than work done during second 50 m fall W

A side wall of a wide open tank is provided with a narrowing tube through which water flows out The cross sectional area of the tube decreases from S 3 0 cm to s 1 0 cm The water level in the tank is h 4 6 m higher than that in the tube Neglecting the viscosity of the water find the horizontal component of the force tending to pull the tube out of the tank S

A solid body floats in liquid at temperature 0 C and is completely submerged in it at 50 C What fraction fo volume of the body is submerged in the liquid at 0 C i Y 0 3x105K2 and of the liquid Y 8 0x10 5K

A vertical venturi meter is installed in a pipeline 30 cm diameter The throat to pipe diameter ratio is 1 3 Water flows through the system The pressure in the pipeline is 140 kN m and vacuum in the throat is 40 mm Hg If 3 of the differential head is lost between the gauges find the flow rate in the pipeline Name the principle on which the venturi meter works 3 1