Mr Rishi Gopie HYDROSTATICS
HYDROSTATICS PRESSURE Pressure (P) is defined as the average force (F) exerted normally per unit area (A), i.e. P = F/A. it is a scalar quantity and its SI unit is Nm - 2 or Pascal Pa. Its concept can be illustrated by placing a solid rectangular block of material, with sides of different lengths, on its various faces and edges and corners. Regardless the face/edge/corner that it rests on its weight (a force) is the same but since the areas are different then so are the pressures that it exerts on whatever surface it rests on. Practical applications of the concept include: inflation of car tyres under various loads, thumbtack design, effect of stiletto- heeled shoes on various surfaces, the difference in effect between dull and sharp knives, the effect of walking on tip toes as opposed to that of walking flat- footedly, the action of ice skates, the action of an ice pick. Fluid pressure A fluid is a liquid or a gas. The pressure in a fluid at rest i) Acts equally in all directions at any given point ii) Is the same at all points in the same horizontal level iii) Does not depend on the area of cross- section of the container holding the fluid (or on the shape of the container) iv) At a given point depends only on the depth, h, of that point within the fluid and on the density, ρ of the fluid and is given by P = h x ρ x g, where P is the pressure measured in Nm - 2 or Pa, h is measured in m, ρ is measured in kgm - 3, and g is the acceleration due to gravity, 10ms - 2 (or gravitational field strength, 10 Nkg - 1 ). This means that pressure increases with depth in a fluid and it explains, for instance, why a water dam is built with a concrete base that is much thicker than its top. Page 2 of 9
HYDRAULIC PRINCIPLE The hydraulic principle, or Pascal s principle, states that pressure is transmitted equally in all directions by a liquid throughout the liquid. This is so since, like a solid (and unlike a gas), a liquid is in compressible Diag. 40 Since A>> a then F>>f and the load = F Page 3 of 9
As a machine the arrangement is a force multiplier The application of the hydraulic principle includes: i) The hydraulic braking systems in motor vehicles ii) The hydraulic jack iii) The hydraulic lift. Page 4 of 9
ATMOSPHERIC PRESSURE The atmosphere is that relatively thin layer of air (a gas). That surrounds the earth. Air has a mass and hence a weight, and this weight acting over the earth`s surface area (and that of objects on the earth) gives rise to atmospheric pressure. The atmosphere however is not of uniform, density since the air becomes thinner, i.e. less dense, with increasing height in the atmosphere (i.e. increasing altitude). So that atmospheric pressure decreases with increasing altitude. Demonstrations of the effects of atmospheric pressure include: i) The crushing can experiment ii) The action of drinking straw iii) The action of syringe iv) The action of rubber suckers v) The action of pumps such as the bicycle pump, the common or lift pump, the force pump vi) The action of the lungs,i.e. respiration (similar in mechanism to blowing a balloon by sucking) vii) The action of a siphon viii) Meteorological effects- such as low pressure regions being indicators of approaching stormy weather (including hurricanes) Page 5 of 9
TUTORIAL 1. You climb a ladder in bare feet. Explain why flat rungs will feel far more comfortable than round ones. 2. Using the words force and pressure correctly, explain why a knife needs to be sharp to cut well. 3. A force of 800 N is spread evenly over an area of 4 m 2. What pressure is acting on the surface? 4. A pressure of 150 N m - 2 is applied to a surface of area 5 m 2. How large is the total force acting on the surface? 5. Each side of a cube measures 2 m. Its weight is 1000 N. If it is placed on a table (a) what force does it exert on the table, and (b) what pressure does it exert on the table? 6. The pressure in a car's tyres is 200 000 N m - 2. The total weight of the car is 10 000 N. Calculate the area of the car's tyres which must be in contact with the ground. Explain your reasoning. Page 6 of 9
7. Fig.10.6 represents a round- bottomed flask which has several tiny holes punctured in it as shown. It is full of water. The piston is pushed down. Copy the diagram and draw on it what happens. Explain why. 8. Fig.10.7 shows a can of water with three tiny holes in it, standing on top of a high wall. Copy the drawing, and show on it the paths of the water jets emerging from the holes. Explain why you have drawn them like that. Page 7 of 9
9. What is the pressure at a depth of 3.0 m below the surface of a liquid of density 1200 kg m - 3? (g = 10 N kg - 1 ) 10. How far must you descend below the surface of a liquid of density 800 kg m - 3 for the pressure to rise by 100 000 N m - 2? 11. Fig.10.8 shows a cross- section of the retaining wall of a large dam. Suggest why it is that shape. Page 8 of 9
12. A pressure gauge, marked in units of N m - 2, is used to record the total pressure at a series of depths h beneath the surface of a liquid in a large tank. These are the readings obtained: Depth h beneath surface of liquid / m 0.25 0.60 1.00 1.45 1.95 2.40 Total pressure / 10 3 N m - 2 105 109 114 119 125 130 (a) Plot a graph of total pressure / 10 3 N m - 2 against depth h / m. (The units for pressure mean that a reading of 120 on the graph, for example, means 120 x 10 3 N m - 2 ). The depth scale should start at zero, but the pressure scale need not do so. (b) Explain why the intercept on the pressure axis gives a value for atmospheric pressure. Write this value down. (c) Find the gradient of the graph. Explain why its units will be N m - 3. (d) Given that this gradient is equal to the density of the liquid multiplied by g, use it to obtain a value for the density of the liquid. Take g to be 9.8 N kg - 1. Show how your calculation leads to the correct units for density, and quote your answer to a suitable number of figures. Page 9 of 9