**Fluids**

- This video introduces the term fluid for liquid and gases and explains how it is different from solids in terms of different characteristic.
- This video explains the concept of pressure and its dependence upon height in case of a fluid, irrespective of the size and shape of the contatiner.
- Water is filled to height h in a inclined vessel as shown in the figure. Find the pressure exerted by water on the bottom face of vessel.
- Water is poured up to same height in the three vessels having the same area of base, as shown in the figure. Is the force exerted by water on the base of vessels equal? Is the weight of water in all the vessels equal?
- This video redefines the pressure as absolute and gauge pressure at a given height of the fluid, considering atmospheric pressure is present at the open surface. It also explains the method used to measure the atmospheric pressure using mercury barometer.
- Consider a rectangular tank of size (l x b x w) filled with a liquid of density ρ to a height H as shown in figure. Find the force at the base and on the walls of the tank. What is the effective point of application of force on the side wall?
- Find the force exerted by the liquid on the side walls of the vessel in the situations shown in the figure. Density of liquid and width of vessel are given.
- Water is contained in a vessel as shown in the figure. Compute the horizontal and vertical components of force due to hydrostatic pressure on the section AB, which is a quarter of a cylinder of radius r. Given the value of r and width of the gate.
- This video illustrates the Pascal’s law which governs the change in pressure for an enclosed, incompressible fluid, through examples of toothpaste tube and motor tyres.
- In a hydraulic press, the cross sectional area of the two cylinders is A1 and A2 respectively. A force F1 is applied to smaller cylinder. (a) What is the pressure produced in the cylinders? (b) What is the thrust exerted on the larger plunger? (c) How much work is done by the operator, if the smaller plunger moves down a distance d1?
- Consider a rectangular tank of size (l x b x w) filled with a liquid of density ρ to a height H as shown in figure. Find the force at the base and on the walls of the tank. What is the effective point of application of force on the side wall?
- Figure shows an L-shaped tube filled with a liquid to a height h. What should be the horizontal acceleration ‘a’ of the tube so that the pressure at the point B becomes atmospheric?
- Find the force exerted by the liquid on the side walls of the vessel in the situations shown in the figure. Density of liquid and width of vessel are given.
- A trolley containing a liquid slides down a smooth plane inclined at an angle with the horizontal as shown in figure. Find the angle of inclination of the free surface of water with the horizontal.
- This video illustrates the situation when a fluid in a container is rotated around a central vertical axis along with equation of the surface, the fluid attains.
- A cylindrical vessel of radius R and height H is filled up to 4H/5 with a liquid of specific gravity ρ. The vessel is rotated about its axis. (a) Determine the speed of rotation when the liquid just starts spilling. (b) Determine the height of lowest point of surface of liquid at the above speed. (c) Find the speed of rotation when the base is just visible.
- Water is filled in a vessel to a height h. A small orifice is made at the bottom of vessel. Find the speed of efflux with which water comes out from the orifice. ( Area of cross-section of orifice is negligible as compared to the area of cross-section of the vessel )
- This video explains the concept of buoyancy which is upward force acting on an object submerged in a fluid and equal to the weight of fluid displaced by it. The object sinks when the buoyant force is less than its weight and vice-versa which is stated in the Archimedes’ principle.
- A wooden object floats in water kept in a beaker. The object is near a side of the beaker. Let P1, P2, P3 be the pressures at the three points A, B and C of the bottom as shown in figure. Which of the following is correct? (a) P1 = P2 = P3 (b) P1 < P2 < P3 (c) P1 > P2 > P3 (d) P1 = P2 ≠ P3
- A piece of wood floats in water kept in a beaker. If the beaker moves with a vertical acceleration a, the wood will (a) sink deeper in the liquid if a is upward (b) sink deeper in the liquid if a is downward, with a < g (c) come out more from the liquid if a is downward, with a < g (d) remain in the same position relative to the water
- A uniform cylinder of density ρ and cross-sectional area A floats in equilibrium in two non-mixing liquids of densities ρ1 and ρ2. The length of the part of the cylinder in air is h and the lengths of the part of cylinder immersed in the liquid are h1 and h2 as shown in the figure. Find the height h. If the cylinder is depressed in such a way that its top surface is just covered with the liquid of density ρ1 and then released, find the force acting on the cylinder and its acceleration.
- A wooden stick of length L, radius R and density ρ has a small metal piece of mass m (of negligible volume) attached to its one end. Find the minimum value for the mass m (in terms of given parameters) that would make the stick float vertically in equilibrium in a liquid of density σ (>ρ).
- This video explains in details the assumption made in study of dynamics of moving fluid like the steady or laminar, streamlined, nonviscous and irrotational flow along with Incompressibility of the fluid. The fluid of such assumed nature is considered ideal.
- This video explains the derivation of Bernoulli’s equation by considering the change in kinetic energy of fluid flowing through a tube.
- Which of the following is correct for streamline flow? (a) the speed of the particle always remains same (b) the velocity of particle always remains same (c) the kinetic energies of all the particles arriving at a given point are the same (d) the momentum of all the particles arriving at a given point are the same.
- Consider a uniform cylindrical tube completely filled with water. Water enters the tube through end A with speed v1 and leaves through end B with speed v2. In case I the tube is horizontal, in case II it is vertical with the end A upward and in case III it is vertical with the end B upward as shown in figure. For which case, speed v1 is equal to seed v2?
- Water flows smoothly through the pipe shown in the figure, descending in the process. Rank the four numbered sections of pipe in decreasing order according to (a) the volume flow rate through them, (b) the flow speed through them and (c) the water pressure at them.
- Water is filled up to a height h in a beaker of radius R as shown in figure. The density of water is ρ, the surface tension of water is T and the atmospheric pressure is Po. Consider a vertical section ABCD of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude….?
- An open U-tube contains two liquids of different densities. If the density of heavier liquid is given, find the density of lighter liquid in terms of the heights of liquids in the arms of tube.
- A U-tube of uniform cross section contains mercury (density ρ) in both of its arms. Liquids of different densities are poured into each arm of the tube until the upper surfaces of both the liquids are in the same horizontal level. If the density of the liquids is η1 and η2 times the density of mercury, find the ratio of heights of the two liquids.
- A circular tube of uniform cross section is filled with two liquids of densities ρ1 and ρ2 such that each liquid occupies a quarter of volume of the tube as shown in figure. If the line joining the interface of liquids makes an angle with vertical, find the value of the angle.
- A solid hemisphere of radius R is made to just sink in a liquid of density ρ. Find the following. (a) the vertical thrust on the curved surface, (b) the side thrust on the hemisphere,(c) the vertical thrust on the flat surface,(d) the total hydrostatic force acting on the hemisphere.
- The vessel shown in figure has two section of areas of cross section A1, and A2. A liquid of density ρ fills both the section up to a height h in each. Neglect air pressure. Find the weight of the liquid and the pressure & force exerted by it on the base. Also find the downward force exerted on the liquid by the wall of the vessel at the level X.
- The weight of a metallic block in air, and when immersed in water is given. It is known that some copper is mixed with the gold. Find the amount of copper added if the densities of gold and copper is known.
- A piece of ice is floating in water. What will happen to the level of water when all ice melts? What will happen if the vessel is filled not with water but with liquid a) denser than water b) lighter than water
- A cubical block of iron with given side length is floating on mercury in a vessel (a) What is the height of the block above mercury level? (b) Water is poured into the vessel so that it just covers the iron block? What is the height of the water column? (Densities of mercury and iron is given)
- A block of wood is floating in water in a closed vessel as shown in the figure. The vessel is connected to an air pump. When more air is pushed into the vessel, the block of wood floats with (neglect compressibility of water) (a) larger part in the water (b) smaller part in the water (c) same part in the water (d) at some instant it will sink.
- A boat floating in a water tank is carrying a large stone as shown in figure. If the stone is unloaded into water, what will happen to the water level?
- A rod of length is hinged at one end at a distance below the water surface as shown in figure. (Specific gravity of the material, length and mass of the rod is given) Find (a) the length of rod under water (b) angle made by rod with the vertical (c) What weight must attached to the other end of the rod so that a given length of the rod is submerged? (d) Find the magnitude and direction of the force exerted by the hinge on the rod.
- A tension in a string holding a solid block below the surface of a liquid as in figure is T when the system is at rest. Then what will be the tension in the string if the system has upward acceleration a?
- A U-tube contains two liquids of densities ρ1 and ρ2 as shown in figure. The tube is now given acceleration ‘a’ in the horizontal direction and the height difference in the sections is as shown. What is the ratio of densities of the two liquids ρ1: ρ2?
- A non-uniform cylinder of mass m, length l and radius r is having its center of mass at a distance l/4 from the center and lying on the axis of the cylinder as shown in figure. The cylinder is kept in a liquid of uniform density ρ. The moment of inertia of the rod about the center of mass is I. The angular acceleration of the point A relative to point B just after the rod is released from the position is….?
- Water is emerging slowly and smoothly from a tap. Find the radius of cross-section of water as a function of depth h fallen from the tap.
- A container of a given width is filled with a liquid. A uniform wire of known mass per unit length is gently placed on the middle of the surface is depressed by a given distance. The surface tension of liquid is ..?
- A vessel with a small orifice at its bottom is field with water and kerosene. Density of water is ρ1 and density of kerosene is ρ2 (ρ1 > ρ2). Find the velocity of water flow if the height of the water layer is h1 and that of the kerosene layer is h2. Neglect viscosity.
- A Venturi-meter is used to measure the flow speed of a fluid in a pipe. The meter is connected between two sections of the pipe; The cross sectional area 'A' of the entrance and exit of the meter matches the pipe’s cross-sectional area. Between the entrance and exit, the fluid flows from the pipe with speed v and then through a narrow region of cross-sectional area 'a' with speed V. A manometer connects the wider portion of the meter to the narrower portion. The change in the fluid’s speed is accompanied by a pressure difference between the wider and narrower region, which causes a height difference h of the liquid in the two arms of the nanometer. Find the speed of flow?
- A pitot tube is mounted along the axis of a gas pipeline having cross-sectional area A. If the densities of the liquid and the gas and the difference in the height of liquid columns in the two arms of the pitot's tube is given, find the speed of gas flowing across the section of the pipe.
- A tube bent at right angle is lowered into a water stream, as shown in figure. The velocity of the steam relative to the tube is v. The closed upper end of the tube situated at a height h0 from the water surface has a small orifice. Find the height h up to which the water jet will spurt.
- Figure shows a Siphon, which is a device for removing liquid from a container. The tube must initially be filled, but once this has been done, liquid will flow through the tube until the liquid surface in the container is in level with the lower end of the tube. Answer the following. (a) with what speed does the liquid emerge from the tube? (b) what is pressure in the liquid at the topmost point of the tube?
- Find the work that has to be done to squeeze all water from a horizontally placed cylinder of volume V through an orifice of cross-sectional area a during the time t by means of constant force acting on the piston as shown in figure. The cross-sectional area of the orifice is considerably less than the piston area and there are no resistive forces.
- Two liquids are filled up to heights h1 and h2 behind a wall of width w as shown in figure. Find out (a) forces in part AB and BC (b) point of application of total force.(neglect atmospheric pressure)
- Length of a horizontal arm of a tube is L and ends of both the vertical arms are open to atmospheric pressure Po. A liquid of density ρ is poured in the tube such that liquid just fills the horizontal part of the tube as shown in figure. Now one end of the open end is sealed and the tube is then rotated about a vertical axis passing through the other vertical arm with angular speed ω. If the liquid rises to a height h in the sealed arm, find the pressure in the sealed tube during rotation.
- A wide cylindrical vessel of height H is filled with water and is placed on the ground. Find at what height h from the bottom of the vessel a small hole should be made in the vessel so that the water coming out of this hole strikes the ground at the maximum distance from the vessel. What is this maximum distance?
- A vessel filled with water is free to slide on a frictionless surface. A small hole is made at a depth h from the surface. What is force required to be applied on the vessel to keep it stationary immediately after the water starts leaking.
- The tube shown is of uniform cross-section. Liquid flows through it at a constant speed in the direction shown by the arrows. Find the direction of net force and torque exerted by liquid on the tube.
- Water is flowing out of a tank through a tube bent at right angle as shown in figure. The radius of the tube is r and the length of its horizontal section is l. The rate of water flow is Q. What is the moment of reaction forces of flowing water acting on the tube's wall, relative to the point O?
- The side wall of a wide vertical cylindrical vessel of height h has a narrow vertical slit with given width running all the way down to the bottom of the vessel. With the slit closed, the vessel is filled with water. What is the resultant force of reaction of the water flowing out of the vessel immediately after the slit is opened?
- A cylindrical vessel of height H and base area A is filled with water. The vessel has a small orifice of area ‘a’ in the bottom. Find the time in which the vessel will get empty.
- This video illustrates the equilibrium of a partially or fully submerged body considering the net torque on it. It defines the stable, neutral and unstable equilibrium in terms of position of centre of gravity, centre of buoyancy and meta centre.