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MECHANICAL PROPERTIES OF FLUIDS 185 Answer Hereh=1000m and ρ=1.03×10 kgm . 3 -3 law. In these devices, fluids are used for (a) From Eq. (9.6), absolute pressure transmitting pressure. In a hydraulic lift, as P =P a ρgh shown in Fig. 9.6 (b), two pistons are separated = 1.01 × 10 Pa by the space filled with a liquid. A piston of small 3 –3 –2 + 1.03 × 10 kg m × 10 m s × 1000 m cross-sectionA i1 used to exert a forceF d1rectly = 104.01 × 10 Pa5 F1 ≈ 104 atm on the liquid. The pressure P = is A1 (b) Gauge pressure is P −P = agh = P g transmitted throughout the liquid to the larger P = 1.03 × 10 kg m × 10 ms × 1000 m cylinder attached with a larger piston of area A , g 5 2 = 103 × 10 Pa which results in an upward force of P × A . 2 ≈ 103 atm Therefore, the piston is capable of supporting a (c) The pressure outside the submarine is large force (large weight of, say a car, or a truck, P =P a ρgh and the pressure inside it is P .a F1A2 Hence, the net pressure acting on the placed on the platform) F = PA = . By window is gauge pressure, P = ρgh. Since 2 2 A1 g 2 changing the force at A , the platform can be the area of the window is A = 0.04 m , the 1 force acting on it is moved up or down. Thus, the applied force has F=P A=103×10 Pa×0.04m =4.12×10 N 5 g A 2 ⊳ been increased by a factor of A and this factor 1 9.2.4 Hydraulic Machines is the mechanical advantage of the device. The example below clarifies it. Let us now consider what happens when we change the pressure on a fluid contained in a vessel. Consider a horizontal cylinder with a piston and three vertical tubes at different points [Fig. 9.6 (a)]. The pressure in the horizontal cylinder is indicated by the height of liquid column in the vertical tubes. It is necessarily the same in all. If we push the piston, the fluid level rises in all the tubes, again reaching the same level in each one of them. Fig 9.6(b)Schematicdiagramillustratingtheprinciple behind the hydraulic lift, a device used to lift heavy loads. Fig 9.6 (a) Whenever external pressure is applied Example 9.5 Two syringes of different on any part of a fluid in a vessel, it is ⊳cross-sections (without needles) filled with equally transmitted in all directions. water are connected with a tightly fitted rubber tube filled with water. Diameters of This indicates that when the pressure on the the smaller piston and larger piston are cylinder was increased, it was distributed uniformly throughout. We can say whenever 1.0 cm and 3.0 cm respectively. (a) Find the force exerted on the larger piston when external pressure is applied on any part of a a force of 10 N is applied to the smaller fluid contained in a vessel, it is transmitted piston. (b) If the smaller piston is pushed undiminished and equally in all directions. in through 6.0 cm, how much does the This is another form of the Pascal’s law and it larger piston move out? has many applications in daily life. A number of devices, such as hydraulic lift Answer (a) Since pressure is transmitted and hydraulic brakes, are based on the Pascal’s undiminished throughout the fluid, Reprint 2026-27