Fluids Questions and Answers

Que 11 Water flows in a horizontal tube as shown in figure The pressure of water changes by 600 N m 2 between A and B where the areas of cross section are 3 cm 2 and 1 5cm 2 respectively The rate of flow of water through the tube is Take 0 4 0 63 A 63 cm 3 s 126 cm 3 s 189 cm 3 s Data Insufficient B

Let P represent the magnitude of the force experienced by a molecule in the free surface of a liquid and in contact with a solid surface whereas Q represents the magnitude of the force experienced by the molecule see the figure The free surface of the liquid will be concave if P Option A B P 9 1 2 P Rate this questi

A container of large uniform cross section area A resting on a horizontal surface holds two immiscible non viscous and incompressible liquid of densities pand 2p Each of height H 2 as shown A tiny hole of area S A is punched on the vertical side of the container at a height h H 2 Initial speed of efflux of the liquid at the hole is Option A B 2p H h gh 2gh 3H 4h g 2 Rate this question

A glass capillary tube of length and inside diameter d is submerged vertically into water The upper en of the capillary is sealed The outside pressure is standard To what length x has the capillary to be submerged to make the water levels inside and outside the capillary coincide S surface tension of water Option A d Po 1 AS 2l Rate this question

A U tube of uniform cross section shown in figure is partially filled with a liquid I Another liquid II which does not mix with liquid I is poured into one side It is found that the liquid levels of the two sides of the tube are the same while the level of liquid I has risen by 2 cm If the specific gravity of liquid I is 1 1 the specific gravity of liquid II must be U Option A B D 1 12 1 1 1 05 10 Rate this question

are 13 A mercury drop on a clean horizontal glass surface and a water drop on a horizontal glass plate coated with a thin layer of talcum powder similar in shape If it is known that for a particular shape of a drop surface energy of surface tension and the gravitational potential energy bear a definite ratio that is independent of the size of the drop estimate the ratio masses of these drops Density of mercury is pH 13 60 g cm density of water is pw 1 00 g cm surface tension of mercury is OH 0 46 N m and surface tension of water is ow 0 07 N m

80 An aluminium sphere is dipped into water Which of the following is true Buoyancy will be less in water at 0 C than that in water at 4 C Buoyancy will be more in water at 0 C than that in water at 4 C Buoyancy in water at 0 C will be same as that in water at 4 C Buoyancy may be more or less in water at 4 C depending on the radius of the sphere

49 The velocity of the surface layer of water in a river of depth 20 m is 5 m s The shearing stress between the surface layer and the bottom layer is n 10 poise 2 5 10 N m b 3 x 10 N m d 4 x 10 N m a c 3 5 x 10 5 N m

42 A water container filled full with water having an orifice at its bottom are placed on the table of height 1 2m from the ground Water is continuously coming out from orifice and covers a distance of 2m What will be the length of water column in the container a 0 83 m b 0 1 m c 0 25m A vessel containing water has area of or d 0 56 m 40

The specific gravity of an object is 0 872 whereas hat of seawater is 1 025 Part A What percent of an object is above the surface of the water Express your answer using three significant figures VAE Valem vi www 0 105 1

1 A vertical tank with depth H is full with water A hole is made on one side of the walls at a depth h below the water surface At what distance from the foot of the wall does the emerging stream of water strike the foot a h H h b 2 h H h c 2 H h h H h d 2h H h 7 8

The hydraulic grade line for flow in a pipe of constant internal diameter fed 31 aug fy EISSTIC DE CIST a coincides with the physical centerline of the Fara pip b is always above the total energy grade line BAR of fas tu 34 ad c is always sloping down in the direction of flow f d is always above the centerline of the pipe 9

The radius of a soap bubble is r The surface tension of soap solution is T Keeping temperature constant the radius of th soap bubble is doubled the energy necessary for this will be O 24 r T 8 T 12 T

c 5m s 25 A wooden plank of length 1 m and uniform cross section is hinged at one end to the bottom of a tank as shown in figure The tank is filled with water up to a height of 0 5 m The specific gravity of the plank is 0 5 Find the angle 0 that the plank makes with the vertical in the equilibrium position F HE B 0 A mg l 0 a 30 b 60 26 A horizontal oriented tube c 45 AR dat d 90

a 30 b 60 c 45 d 90 26 A horizontal oriented tube AB of length 5 m rotates with a constant angular velocity 0 5 rad s about a stationary vertical axis OO passing through the end A The tube is filled with ideal fluid The end of the tube is open the closed end B has a very small orifice The velocity with which the liquid comes out from the hole in m s is a 1 m s A O b 2 m s 5m 2m c 4 m s d 3 m s

According to Bernoulli s equation below the product of the area A of a cross section of a hose at a particular point and the velocity V of water travel the product of the area A of a second cross section of the same hose at a second point and the velocity V of water traveling through the hose at the A V A V 1 f someone covers of the opening of a hose how will the velocity of the water coming out of the hose change of the velocity through the full opening A The velocity of the water through the partially covered opening will be 3 The velocity of the water through the partially covered opening will be of the velocity through the full opening of the velocity through the full opening 3 C The velocity of the water through the partially covered opening will be Q The velocity of the water through the partially covered opening will be 4 times the velocity through the full opening

A metallic square plate EFGH is suspended vertically with a pair of sides horizontal by a light inelastic string shown in the figure A beaker of the water is brought below the plate and raised till the plate is completely immersed and the level of the water is above the plate If the point of support is slowly raised vertically at a constant velocity the graph of tension T in the string against the displacements of the point support is represented by A B C T TA 11 Correct Answer T 11 H S S

Mechanical Properties of Solids 36 A light rod of length 2 m is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends One of the wires is made of steel and is of cross section 0 1 cm and the other of brass of cross section 0 2 cm Along the rod at what distance a weight may be hung to produce equal stresses in both the wires 2 x 10 Nm2 Yra1x 10 Nm m from brass wire a m from steel wire b c 1 m from steel wire d m from brass wire 37 In the question number 36 at which distance a wright may be hung along the rod in order to in both the wires a 0 0 43 A stee before anoth radiu befor a 44 Au sect one cor YE inc

37 A vessel containing water stand on a table of height H A small hole is punched in the side of vessel at its base The steam of water strikes the ground at a horizontal distance R from the table Then the depth of water in the cylinder is a H c VRH b R d R 4H

34 In a hydraulic lift force F isexerted on small cylinder A of radius 7cm This pressure is transmitted to a second cylinder of radius 14cm through a pipe C If the car is to be lifted is 1500 kg What is the pressure applied to cylinder A a 1kPa c 354 10 Pa A C B b 3 106 Pa d 382 10 Pa

liquid in capillary tube always remains constant 5 Assertion A thin stainless steel needle can lay floating on a still water surface Reason Any object floats when buoyancy force balances the weight of the object

1 Assertion At critical temperature surface tension of a liquid becomes zero Reason At this temperature intermolecular forces for liquids and gases become equal Liquid can expand without any restriction

In the figure shown water is filled in a symmetrical container Four pistons of equal area A are used at the four openings to keep the water in equilibrium Now an additional force F is applied at each piston The increase in the pressure at the centre of the container due to this addition is F F

13 Consider two identical cylindrical vessels one filled up to a height 1 0 m by a large number of plastic beads and the other filled up to same height by water Total mass of the beads is m 500 kg and th the water is M 1000 kg If all the water is gradually transferred in first vessel find height attained by the top layer of the beads Der of the plastic is p 800 kg m and that of water is po 1000 kg m

Is the below statement is correct for Venturi meter pls give explaination In the same Venturi meter two different values of the imposed pressure drop result in two different values of the manometer deflection

16 One half of a rod of length 1 100 cm has density P 0 50 g cm and the other half has density p 2 50 g cm The rod is placed on horizontal bottom of a large tub and then water is gradually poured in the tub Find the depth of water in the tub when the rod makes angle 53 with the horizontal Density of water is p 1 00 g cm

20 A tube made of very thin glass sheet has mass m length 1 and cross section area S Its lower end is closed Up to what height h should water be filled in the tube so that it can float vertically in water Density of water is po

A homogeneous beam of length and square section of side leng held horizontally so that one of its long faces touches water in reservoir Density of material of the beam pis equal to density of The beam is released Find the amount of heat developed until perturbations cease Acceleration of free fall is g oulindrical tubo is fitted coovially at one of its ondo int n hold

3 Assertion When a gas is allowed to expand work done by gas is positive Reason In expansion of a gas the force due to gaseous pressure and displacement of piston are in the same direction

A uniform cylinder made of a material of density p 250 kg m is held at rest in a pool so that its upper circular surface is in level with the water surface Length of the cylinder is 1 20 cm and radius is r 3 0 cm When released the cylinder jumps out of water moving vertically Find velocity with which the cylinder leaves the water surface Density of water is po 1000 kg m and acceleration due to gravity is g 10 m s Neglect all dissipative effects

3 A piece of cork is floating on water in a small tank The cork oscillates up and down vertically when small ripples pass over the surface of water The velocity of the ripples being 0 21 ms wavelength 15 mm and amplitude 5mm the maximum velocity of the piece of cork is a 0 44 ms b 0 24 ms c 2 4 ms 1 d 44 ms 1

the horizontal Density of water is p 1 00 g cm 17 A wooden cylinder of cross section area S is connected with the bottom of a vessel by a spring of stiffness k 10 N m When some water is filled in the vessel the cylinder floats partially submerged and extension in the spring becomes xo Density of water is pw and acceleration of free fall is g If the vessel is given an upwards acceleration a by what amount will the length of the submerged portion of the cylinder change

A tank of height H is fully filled with water If the water rushing from a made in the tank below the free surface strikes the floor at maximum horizontal distance then depth of the hole from the free surface must be

A U tube containing two different liquid of density p and 2p is fixed vertically on a rotating table as shown in the figure Initially table is at rest and table can rotate about a vertical axis passing through the centre of the table The interface of two liquids of densities p and 2p respectively lies at the point A in a U tube at rest The height of liquid column above A is 3 where AB 2a The cross sectional area of the tube is S Now the table is whirled with angular velocity w about a vertical axis as shown in figure such 8 2 that the interface of the liquids shifts towards B by 3 then at this instant Find the force exerted by liquid of p on liquid of 2p at the interface A 2p

180 kg 2 50 kg 3 60 kg At what speed the velocity head of water is equal to pressure head of 40 cm of hg 1 10 3 m s 2 2 8 m s 3 5 6 m s 4 8 4 m s A hole is in the bottom of the tank having water If total pressure at the bottom is 3 atm 1 atm 105 Nm RPMT 20 RPMT 200

A long square wooden block is pivoted along one edge as shown The block is in equilibrium when immersed in water to the depth shown D d 0 6m Water L Air L 1 2m Pivot O Assuming friction in the pivot is negligible Let the density of wood be 170g Hence a is in Sl unit up to two significant digit

Two metal spheres are falling through a liquid of density 2 x 10 kg m with the same uniform speed The material density of sphere 1 and sphere 2 are 8 10 3 kg m and 11 x 103 kg m respectively The ratio of their radii is O 11 8

7 34 An open rectangular tank 1 5 m wide 2m deep and 2m long is half filled with water It is accelerated horizontally at 3 27 m sec in the direction of its length Determine the depth of water at rear end of tank g 9 81 m sec2 A 0 9m B 1 2m C 1 5m D 1 7m

12 A container with square base of side a is filled up to a height H with a liquid A hole is made at a depth h from the free surface of water With what acceleration the container must be accelerated so that the water does not come out a g C 2gH 2 b g 2 d 2gH 20

3 A vessel containing water has area of cross section 16 cm A small square hole of side 1 cm is at the bottom What will be the time taken by the water to empty the vessel if vessel is filled up to the height of 32 cm g 9 8 m s a 3 sec b 5 sec c 4 sec d 8 sec

5 Two parallel glass plates are dipped partly in the liquid of density d keeping them vertica the distance between the plates is x surface tension for the liquid is T and angle of conta then rise of liquid between the plates due to capillary will be T cos 0 2T cose 6 8 xd 27 d xdg T cose

5 A uniform sphere of mass m and another uniform hemisphere of the same material and radius r are placed in a vessel In the vessel water is filled up to height r 30 0 cm as shown There is no water or air under the hemisphere The sphere and the hemisphere both are connected with vertical threads to the ends of a light rod AB of length 116 cm having a hinge O Find the distance of the hinge from the end A so that when an upward minimum pull is applied at the hinge the sphere and the hemisphere both will simultaneously leave the bottom of the vessel Density of the material of the sphere is p 5 0 g cm and that of water is po 1 0 g cm D B

23 In the given figure the container slides down with acceleration a on an incline of angle 0 Liquid is stationary with respect to container Find out angle made by surface of liquid with horizontal plane if a g sine a 20 c 30 b 0 d tan 30 0 27

29 Two drops of the same radius are falling through air with a steady velocity of 5cm s If the two drops coalesce the terminal velocity would be 1 10 cm s 2 2 5 cm s 4 5x 3 cm s Key 3 Solution If R is radius of bigger drop formed then 3 5x 4 3 cm s

Consider the system shown in the figure A ball of density o is tied to the bottom of the bucket which contains a liquid of density p p o The volume of the ball is V and the mass of bucket along with its contents is 2M The system is released from rest The thread connected to the ball is taut The tension in the thread connected to the ball will be M w 2M Rate this question

A vessel of large area of cross section opened at the top has a small hole at its bottom and is 3 completely filled with water When the hole at the bottom is opened of volume of water 4 1 comes out in time t The time 1 taken for the remaining of the water to come out is equal to 4 1 t 4 4 2 4 4 3

A vessel of large uniform cross sectional area resting on a horizontal surface holds two immiscible non viscous incompressible liquids of densities d and 2d each of height H 2 If a H small hole is punched on the vertical side of the container at a height h h from the 2 bottom of the vessel the efflux speed of the liquid through the hole is 1 2g H h 2 g H h 3 3H 4h 4 4H 3h

The area of cross section of a current carrying conductor is Ao and at section 1 and 2 respectively If V V and E 4 E2 be the drift velocity and electric field at section 1 and 2 respectively then 1 1 I 2 V V 1 4 and E E 4 1 XV V 4 1 and E E 1 2 V V 2 1 and E E 1 4 V V 1 4 and E E 1 4

An open U tube contains mercury When 11 2cm of water is poured into one of the arms of the tube how high does the mercury rise in the other arm from its initial level Given Pw 1 g cc PHg 13 6 g cc Question Type Single Correct Type 1 0 56 cm 2 1 35 cm 3 0 41 cm 4 2 32 cm

A vessel containing water is given a constant acceleration a towards the right along a straight horizontal path Which of the following diagram represents the surface of the liquid INT C A Question Type Single Correct Type 1 A 2 B B D a