FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
EXERCISE # (S-1)
HCV Worked out Examples (Chapter No.13 - {3,4,5,7,8})
1. A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an
acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density . Find
the gauge pressure at the centre of the cubical vessel
L
L
a
2. A liquid of density is filled in a U-tube, whose one end is open & at the other end a bulb is
fitted whose pressure is PA. Now this tube is moved horizontally with acceleration 'a' as shown
in the figure. During motion it is found that liquid in both column is at same level at
equilibrium. If atmospheric pressure is P0, then find the value of PA
a PA
3. There are three immiscible liquids of densities 1, 2 and 3. If the first two liquids are taken
in a U–tube then they stand like fig(i). When all the three liquids are taken in U–tube, they
stand like fig(ii). Find the ratio of the densities of the three liquids.
4. For the system shown in the figure, the cylinder on the left at L has a mass of 600kg and a cross
sectional area of 800 cm2. The piston on the right, at S, has cross sectional area 25cm2 and
negligible weight. If the apparatus is filled with oil.( = 0.75 gm/cm3) Find the force F required
to hold the system in equilibrium.
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
5. Dams at two different locations are needed to form a lake. When the lake is filled, the water
level will be at top of both dams. The second dam is twice as high and twice as wide as the first
dam. The force of the water on the second dam is how much greater than the force on the first?
(Ignore atmospheric pressure since it is pushing on both sides of the dams.)
6. As the drawing illustrates, a pond full of water has the shape of an inverted cone with the tip
sliced off and has a depth of 30m. The atmospheric pressure above the pond is 1.0 ×105 Pa. The
circular top surface (radius = R2) and circular bottom surface (radius = R1) of the pond are both
parallel to the ground. The magnitude of the force acting on the top surface is the same as the
R
magnitude of the force acting on the bottom surface. Obtain 2 .
R1
R2
30 m
60.0°
R1
7. A container of a large uniform cross-sectional area A resting on a horizontal surface holds two
H
immiscible, non viscous and incompressible liquids of densities d and 2d each of height as
2
shown. The lower density liquid is open to atmosphere. A homogeneous solid cylinder of
H A
length L cross-sectional area is immersed such that it floats with its axis vertical to
2 5
L
the liquid -liquid interface with length in denser liquid. Find the density of the solid
4
cylinder.
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
d 3L/4 H/2
L/4
2d H/2
8. A liquid of density 2 is filled in a cylindrical vessel, whose cross-sectional area is 2A. A
wooden cylinder of height H, cross-sectional area A and density is floating in the liquid at
equilibrium with its axis vertical. The cylinder is pushed down by a small distance x from its
equilibrium position and released. Find its initial acceleration.
9. In air an object weighs 15N, when immersed completely in water the same object weighs 12N.
When immersed in another liquid completely, it weighs 13N. Find
(a) the specific gravity of the object and
(b) the specific gravity of the other liquid.
10. An expansible balloon filled with air floats on the surface of a lake with 2/3 of its volume
submerged. How deep must it be sunk in the water so that it is just inequilibrium neither
sinking further nor rising? It is assumed that the temperature of the water is constant & that the
height of the water barometer is 9 meters.
11. A wooden plank of length 1 m and uniform cross-section is hinged at one end to the bottom of
a tank as shown. The tank is filled with water upto a height of 0.5 m. The specific gravity of the
plank is 0.5. Find the angle made by the plank in equilibrium position
0.5
12. A spherical tank of 1.2 m radius is half filled with oil of relative density 0.8. If the tank is given
a horizontal acceleration of 10 m/s2. Calculate the inclination of the oil surface to horizontal
and maximum pressure on the tank.
HCV Exercises (Chapter No.13- {2,4,8,11,14,16,18,20,23,25})
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
HCV Worked out Examples(Chapter No.13 - {9,10,11})
13. A jet of water having velocity = 10 m/s and stream cross-section = 2 cm2 hits a flat plate
perpendicularly, with the water splashing out parallel to plate. Find the force that the plate
experiences.
14. A laminar stream is flowing vertically down from a tap of cross-section area 1 cm2. At a
distance 10cm below the tap, the cross-section area of the stream has reduced to 1/2 cm2. Find
the volumetric flow rate of water from the tap.
15. Calculate the rate of flow of glycerin of density 1.25 × 103 kg/m3 through the conical section of
a pipe if the radii of its ends are 0.1m & 0.04m and the pressure drop across its length is
10N/m2.
16. A large cylindrical tank of cross-sectional area 1m2 is filled with water. It has a small hole at a
height of 1m from the bottom. A movable piston of mass 5 kg is fitted on the top of the tank
such that it can slide in the tank freely. A load of 45 kg is applied on the top of water by piston,
as shown in figure. Find the value of v when piston is 7m above the bottom (g = 10 m/s2)
45kg
V
17. For the arrangement shown in the figure. The time interval in seconds after which the water jet
ceases to cross the wall is found to be (A)3. Area of the cross section of the tank A 5 m2
and area of the orifice a=32 cm2. [Assume that the container remaining fixed]. Find the value of
a. (Take g = 10 m/s2)
18. Water fills a reservoir, open to the atmosphere, to height H = 5m above the centerline of a
horizontal exit pipe at the bottom of the reservoir. The first section of the pipe has radius r 1 = 2
cm, the unknown velocity there is v1 and this section of the pipe has a manometer in which the
water rises to an unknown
height h above the centerline of the pipe.
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
EXERCISE # (S-1)
HCV Worked out Examples (Chapter No.13 - {3,4,5,7,8})
1. A cubical sealed vessel with edge L is placed on a cart, which is moving horizontally with an
acceleration ‘a’ as shown in figure. The cube is filled with a ideal fluid having density . Find
the gauge pressure at the centre of the cubical vessel
L
L
a
2. A liquid of density is filled in a U-tube, whose one end is open & at the other end a bulb is
fitted whose pressure is PA. Now this tube is moved horizontally with acceleration 'a' as shown
in the figure. During motion it is found that liquid in both column is at same level at
equilibrium. If atmospheric pressure is P0, then find the value of PA
a PA
3. There are three immiscible liquids of densities 1, 2 and 3. If the first two liquids are taken
in a U–tube then they stand like fig(i). When all the three liquids are taken in U–tube, they
stand like fig(ii). Find the ratio of the densities of the three liquids.
4. For the system shown in the figure, the cylinder on the left at L has a mass of 600kg and a cross
sectional area of 800 cm2. The piston on the right, at S, has cross sectional area 25cm2 and
negligible weight. If the apparatus is filled with oil.( = 0.75 gm/cm3) Find the force F required
to hold the system in equilibrium.
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
5. Dams at two different locations are needed to form a lake. When the lake is filled, the water
level will be at top of both dams. The second dam is twice as high and twice as wide as the first
dam. The force of the water on the second dam is how much greater than the force on the first?
(Ignore atmospheric pressure since it is pushing on both sides of the dams.)
6. As the drawing illustrates, a pond full of water has the shape of an inverted cone with the tip
sliced off and has a depth of 30m. The atmospheric pressure above the pond is 1.0 ×105 Pa. The
circular top surface (radius = R2) and circular bottom surface (radius = R1) of the pond are both
parallel to the ground. The magnitude of the force acting on the top surface is the same as the
R
magnitude of the force acting on the bottom surface. Obtain 2 .
R1
R2
30 m
60.0°
R1
7. A container of a large uniform cross-sectional area A resting on a horizontal surface holds two
H
immiscible, non viscous and incompressible liquids of densities d and 2d each of height as
2
shown. The lower density liquid is open to atmosphere. A homogeneous solid cylinder of
H A
length L cross-sectional area is immersed such that it floats with its axis vertical to
2 5
L
the liquid -liquid interface with length in denser liquid. Find the density of the solid
4
cylinder.
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
d 3L/4 H/2
L/4
2d H/2
8. A liquid of density 2 is filled in a cylindrical vessel, whose cross-sectional area is 2A. A
wooden cylinder of height H, cross-sectional area A and density is floating in the liquid at
equilibrium with its axis vertical. The cylinder is pushed down by a small distance x from its
equilibrium position and released. Find its initial acceleration.
9. In air an object weighs 15N, when immersed completely in water the same object weighs 12N.
When immersed in another liquid completely, it weighs 13N. Find
(a) the specific gravity of the object and
(b) the specific gravity of the other liquid.
10. An expansible balloon filled with air floats on the surface of a lake with 2/3 of its volume
submerged. How deep must it be sunk in the water so that it is just inequilibrium neither
sinking further nor rising? It is assumed that the temperature of the water is constant & that the
height of the water barometer is 9 meters.
11. A wooden plank of length 1 m and uniform cross-section is hinged at one end to the bottom of
a tank as shown. The tank is filled with water upto a height of 0.5 m. The specific gravity of the
plank is 0.5. Find the angle made by the plank in equilibrium position
0.5
12. A spherical tank of 1.2 m radius is half filled with oil of relative density 0.8. If the tank is given
a horizontal acceleration of 10 m/s2. Calculate the inclination of the oil surface to horizontal
and maximum pressure on the tank.
HCV Exercises (Chapter No.13- {2,4,8,11,14,16,18,20,23,25})
, FLUID
BY PRAVEEN KUMAR PACHAURI (PKR SIR, IIT BOMBAY)
IIT- JEE- 2020- 2021
Referral coode - PPLIVE
HCV Worked out Examples(Chapter No.13 - {9,10,11})
13. A jet of water having velocity = 10 m/s and stream cross-section = 2 cm2 hits a flat plate
perpendicularly, with the water splashing out parallel to plate. Find the force that the plate
experiences.
14. A laminar stream is flowing vertically down from a tap of cross-section area 1 cm2. At a
distance 10cm below the tap, the cross-section area of the stream has reduced to 1/2 cm2. Find
the volumetric flow rate of water from the tap.
15. Calculate the rate of flow of glycerin of density 1.25 × 103 kg/m3 through the conical section of
a pipe if the radii of its ends are 0.1m & 0.04m and the pressure drop across its length is
10N/m2.
16. A large cylindrical tank of cross-sectional area 1m2 is filled with water. It has a small hole at a
height of 1m from the bottom. A movable piston of mass 5 kg is fitted on the top of the tank
such that it can slide in the tank freely. A load of 45 kg is applied on the top of water by piston,
as shown in figure. Find the value of v when piston is 7m above the bottom (g = 10 m/s2)
45kg
V
17. For the arrangement shown in the figure. The time interval in seconds after which the water jet
ceases to cross the wall is found to be (A)3. Area of the cross section of the tank A 5 m2
and area of the orifice a=32 cm2. [Assume that the container remaining fixed]. Find the value of
a. (Take g = 10 m/s2)
18. Water fills a reservoir, open to the atmosphere, to height H = 5m above the centerline of a
horizontal exit pipe at the bottom of the reservoir. The first section of the pipe has radius r 1 = 2
cm, the unknown velocity there is v1 and this section of the pipe has a manometer in which the
water rises to an unknown
height h above the centerline of the pipe.
