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Viscosity Determination of a given liquid viscosity Objectives:to determine of a given liquid viscosity using the falling ball method Theory: Viscosity is the quantity that describes a fluid's resistance to flow. Fluids resist the relative motion of immersed objects through them as well as to the motion of layers with differing velocities within them. Water characterized by a lower viscosity (lower friction force between its different layers), while honey is characterized by a higher viscosity (higher friction force between its different layers). Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity) With the exception of superfluids, all real fluids have some internal resistance to flow and therefore are viscous. A fluid which has no resistance to flow is known as an ideal fluid or inviscid fluid. In common usage, a liquid with the viscosity less than water is known as a mobile liquid, while a substance with a viscosity substantially greater than water is simply called a viscous liquid. The study of flowing matter is known as rheology, which includes viscosity and related concepts. Let a ball of radius R with densityο² (kg/m3) moves with a constant terminal velocity v (m/s) in a liquid of density ο²' (kg/m3) as shown in the figure 1. The summation of the forces acting on the ball is equal zero. Buoyant force + Friction force Gravitational Force Figure 1. The forces acting on the ball that is moving with terminal velocity in a viscous liquid. Therefore total upright forces and downright forces have to be the same. Gravitational force = Buoyant force + Friction force Where Gravitational Force = mg = Buoyant Force = 4 3 3 π π 3 ππ π π 3 πβ² π Friction Force = fv = 6 ο°ο¨Rv Where 4 (Stokes' law) ο¨: viscosity coefficient of the liquid in R: radius of the ball (Pa.s.) f: friction coefficient So, 4 3 π π 3 ππ = 4 3 π π 3 πβ² π + 6ο°ο¨RV The above equation can be rewrite to get the coefficient of viscosity ο¨ : πππΉπ ο¨= ( ππ ) (π β πβ² ) Pa.s. Equipment: 1- Cylinder contains metallic ball and liquid of unknown viscosity 2- Stopwatch 3- Metre ruler 4- Micrometer screw gauge Procedure 1- Measure the temperature of the liquid by using of the thermometer fixed in the outer tube (normally 25 C) 2- Measure the radius of the ball (R) by using of micrometer (repeat three times) 3- Measure the time the ball need to fall a distance 10 cm. 4- Repeat step 3 three time and take the mean value of the time. 5- then calculate the velocity v (m/s) (repeat three times) 6- Givens: density of the boron-glass ball ο² = 2200 kg/m3 the density of a 40 % sugar solution ο²' = 1180 kg/m3. Gravity = 9.8 m/s2 7- The tube filled with the liquid is titled by an angle of 10°, therefore the viscosity coefficient will be calculated from the relation: ο¨= πππΉπ ( ππ Results: R = 0.7 cm t1 = S t2 = S t3 = S Mean time t = (t1 + t2 + t2)/3 Velocity = 10 cm/t = ο¨= ) (π β πβ² )cos 10 Pa.s.