Fluid dynamics questions | form five Physics

1. Explain the terms lines of flow and streamlines when applied to fluid flow and deduce the relationship between them in laminar flow.
2. State Bernoulli`s equation , define the physical quantities which appear in it and the conditions required for its validity.
3. The depth of water in a tank of large cross-sectional area is maintained at 20 cm and water emerges in a continuous stream out of a hole 5 mm in diameter in the base.

Calculate:

1. The speed of efflux of water from the hole,
2. The rate of mass flow of water from the hole Given that density of water is 1.00 x 10³ kgm^-3

1. Distinguish between static pressure, dynamic pressure and total pressure when applied to streamline (laminar) fluid flow and write down expressions for these three pressures at a point in the fluid in terms of the flow velocity , the fluid density , pressure p and the height h, of the point with respect to a datum.
2. Describe , with the aid of a labelled diagram, the Pitot-static tube and explain how it may be used to determine the flow velocity of an incompressible, non-viscous fluid.
3. The static pressure in a horizontal pipeline is 4.3 x 10⁴ Pa, the total pressure is 4.7 x 10⁴ Pa, and the area of cross-section is 20 cm² . The fluid may be considered to be incompressible and non-viscous and has a density of 10³kg m^-3.

Calculate

1. The flow velocity in the pipeline
2. The volume flow rate in the pipeline.

Air flows over the upper surfaces of the wings of an aeroplane at a speed of 120.0ms^-1, and past the lower surfaces of the wings at 120.0ms^-1. Calculate the lift force on the aeroplane if it has a total wing area of 20.0m². (density of air=1.29kgm^-3)

A large tank contains water to a depth of 1.0m. Water emerges from a small hole in the side of the tank 20cm below the level of the surface. Calculate:

1. The speed at which the water emerges from the hole,
2. The distance from the base of the tank at which the water strikes the floor on which the tank is standing.

If a second hole were to be drilled in the wall of the tank vertically below the first hole, at what height above the base of the tank would this second hole have to be if the water issuing from it were to hit the floor at the same point as that from the first hole?

The principle of fluid pressure which is used in hydraulic brakes, is the

1. Pressure is the same at all levels in a fluid
2. Increase of pressure is transmitted equally to all parts of a fluid
3. The pressure at a point in a fluid is due to the weight of the fluid above it.
4. Increase of pressure can only be transmitted trhough fluids.
5. The pressure at a given depth is proportional to the depth in the fluid.

1. With the aid of a diagram describe a simple laboratory experiment to measure Young`s modulus of a wooden bar acting as a loaded cantilever from its period of vibration given that the depression S is given by
2. Two small spheres each of mass 10g are attached to a light rod 50cm long . The system is set into oscillation and the period of torsional oscillation is found tobe 770seconds. To produce maximum torsion to the system two larger spheres each of mass 10 kg are placed near each suspended sphere, if the angular deflection of the suspended rod is   rad and the distance between the centers is of the large spheres is 10cm, determine the value of the universal constant of graviation ,G, from the given information.
3. Write the Continuity and Bernoullis` equations as applied to fluid dynamics.
4. i. )Under what conditions is Bernoullis` equation applicable?

ii.)Discuss two(2) applications of the Bernoullis`equation

5. i.)Developan equation to determine the velocity of a fluid in a venture meter pipe.

ii.)What amount of fluid passes through a section at any given time?

a) i. Give the meaning of the terms velocity gradient , tangential stress and coefficient of viscosity as used in fluid dynamics .

2. Write stroke`s equation defining clearly the meaning of all symbols used.
3. State two assumptions used to develop the equation in a) (ii) above

2. Calculate the terminal velocity of the rain drops falling in air assuming that the flow is laminar, the rain drops are spheres of diameter 1mm and the coefficient of viscosity,
3. Water flows past a horizontal plate of area .If its velocity gradient and coefficient of viscosity adjacent to the plate are and respectively, calculate the force acting on the plate.
4. A horizontal pipe of cross sectional area has one section of cross sectional area . If water flows through, and the pressure difference between the two sections is 300Pa, how many cubic meters of water will flow out of the pipe in 1 minute?

State two factors which determine the magnitude of viscous force.

Identify two limitations and three importances of applying Stokes’ law in fluids motion.

Identify two limitations and three importances of applying Stokes’ law in fluids motion.