LESSON 3.2 Understanding pressure in liquids

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Roland Alexander
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1 LESSON 3.2 Understanding pressure in liquids Introduction Liquids have pressure because of their weights. For example, if you try to put your finger over the end of a tap when it is turned on, you can feel the pressure of the water in the pipe. This is just caused by the weight of water in the pipes all the way back up to the cold water in the loft. The force of gravity acts on liquids, pulling them downwards into the container. alculating pressure in a liquid Say that a vertical column of liquid with a density ρ and a horizontal area. onsider an object is placed at point X at a depth h below the surface area of the liquid. The pressure in the liquid is not dependent on the surface area and the shape of a container. Example 1 If the density of sea water is 1150 kgm-3,calculate the pressure below 40 m of sea water due to the water alone. P= 1150 x10 x 40 P = 4.6 x 10 5 Example 2 The figure shows a cylinder containing liquid mercury. What is the pressure caused by the liquid mercury at the point P? [ Density of liquid mercury is 1.36 x 10 5 kg m -3 ] The pressure P due the liquid exerted on the object at point X can be written as: P = F = W = mg (because W = mg) = ρ V g (because ρ = m ) V = ρ h g (because V = h) = ρ h g From the final expression, we can say that the pressure at any point in a liquid at rest is directly proportional to the density of liquid and the depth. P = 1.36 x 10 5 x 10 x 0.6 P= 8.16 x 10 5 Example 3 The pressure of hot water emerging from a tap is 1 x 10 5 Pa. What is the force exerted by the water on a person s thumb,if the person places his thumb over the outlet of the tap and stops the hot water flowing. [ The area of the tap is 10-4 m 2 ] F? 10 N 1

2 pplications of pressure in liquids 1 Water tank Normally a water tank is placed at higher level so as to supply water at greater pressure. 2 Dam The wall of a dam is much thicker at the bottom than at the top because it must withstand the increased lateral pressure in depths of the water. 3 Submarine Submarine is built with thick wall so as to withstand enormous pressure at greater depth Pa, What is the value of L? (Density of water = 1000 kg m - 3 ) 10 cm 20 cm 40 cm D 60 cm E 80 cm 4 The figures show liquids in containers. Which column of liquid exerts the greatest pressure on the base of its container? TUTORIL n air bubble is at a depth of 5 m below the surface of a lake. What is the pressure of water on the bubble if the density of the water is kg m -3? 5 x 10-4 Pa 5 x 10-3 Pa 2 x 10 2 Pa D 5 x 10 3 Pa E 5 x 10 4 Pa 2 The figure shows a cylinder containing oil with a density of 800 kg m -3. What is the pressure caused by the oil at point X? 4.0 x 10 1 N m x 10 2 N m x 10 3 N m -2 D 4.0 x 10 3 N m -2 E 1.6 x 10 4 N m -2 3 The figure shows a high tin with a length of 100 cm is filled to the full with water. 5 Which one of the following is not true? D depth density of the water area of contact the gravitational acceleration 6 The figure shows a polystyrene block being pushed to a depth of h cm from the water surface. P is the water pressure acting on surface Q. If the pressure caused by the water at point P is 2

Which graph shows the relationship between P and h when the block is pushed deeper into the water?

The pressure caused by the water at base of the wooden blocks J, K and L are X 1, X 2 and X 3 respectively.

Which comparison is correct? X 1 > X 2 > X 3 X 1 < X 2 < X 3 X 1 =X 2 = X 3 10 The figure shows a siphon system. Which comparison is correct?

3 Which graph shows the relationship between P and h when the block is pushed deeper into the water? 9 The figure shows three wooden blocks J,K and L are pressed into the water until the base of its reach at level P. The pressure caused by the water at base of the wooden blocks J, K and L are X 1, X 2 and X 3 respectively. 7 The figure shows three containers with different shapes filled with water with the same level. The pressure caused by the water at point P, Q and R are P 1, P 2 and P 3 respectively. Which comparison is correct? X 1 > X 2 > X 3 X 1 < X 2 < X 3 X 1 =X 2 = X 3 10 The figure shows a siphon system. Which comparison is correct? P 1 > P 2 > P 3 P 1 < P 2 < P 3 P 1 =P 2 = P 3 8 Equal masses of water are poured into four jars as shown. In which jar is the pressure exerted by the water on the base the greatest? Which of the following is true? D Water in beaker flows into beaker until the volume of water in beaker is the same as the volume of water in beaker Water in beaker flows into beaker until the level of water in beaker is the same as the level of water in beaker Water in beaker flows into beaker until beaker is full Water in beaker flows into beaker until beaker is empty 3

11 The wall of a dam is much thicker at the bottom than at the top because pressure of water at the upper level is higher than pressure of water at the deeper level pressure of water at the upper

4 11 The wall of a dam is much thicker at the bottom than at the top because pressure of water at the upper level is higher than pressure of water at the deeper level pressure of water at the upper level is lower than pressure of water at the deeper level pressure of water at the upper level is the same as than pressure of water at the deeper level the hot flowing. alculate the force exerted by the water on his thumb. 13 Figure(a) shows an apparatus is used to remove water from a beaker to a cyclinder.the volume of the water in the beaker is same as the volume of water in the cylinder. 12 Figure shows the surface of the water in a domestic cold water tank is 5 m above the downstairs cold water tap. [ tmospheric pressure = Pa ] [ Density of water = 1000 kgm -3 ] Figure (a) (a) (i) Name the system for removing the water. (a) State the principle is used causes the water shoots out from the tap (b) What is the pressure caused by the water in the tank only? (c) What is the pressure of the hot water emerging from the tap? (b) (ii).. Explain how the water flows from the beaker to the cylinder. The water in the beaker stops to flow when the level of the water at P as shown in Figure (b) (d) The area of water tap where water emerges is 0.04 m 2. man places his thumb over the outlet of the tap and stops 4

14 Figure (a) and Figure (b) shows two positions of a diver in the sea. (i) (ii) (iii) Figure (b) Mark the water level in the cylinder in Figure(b) when the water stops to flow.

5 14 Figure (a) and Figure (b) shows two positions of a diver in the sea. (i) (ii) (iii) Figure (b) Mark the water level in the cylinder in Figure(b) when the water stops to flow. Why does the water stop to flow?... y using the same apparatus, suggest one method to remove all the water into the cylinder. Figure(a) Figure(b) Observe the positions of the diver and the pain in his ear. ased on the observations: (a) State one suitable inference that can be made. (b) State one appropriate hypothesis for an investigation. (c) With the use of apparatus such as a high tin, rubber stoppers, and other apparatus, describe an experimental framework to test your hypothesis. In your description, state clearly the following: (i) im of the experiment (ii) Variables in the experiment (iii) List of apparatus and materials (iv) rrangement of the apparatus (v) The procedure of the experiment which include the method of controlling the manipulated variable and the method of measuring the responding variable. (vi) Way you would tabulate the data (vii) Way you would analysis the data 5

L 13 Fluid Statics [2] More on fluids. How can a steel boat float. A ship can float in a cup of water! Today s weather

L 13 Fluid Statics [2] More on fluids. How can a steel boat float. A ship can float in a cup of water! Today s weather The deeper you go the higher the pressure P Top A hypothetical volume of water inside