1. Define the following terms a) Mass density b) Specific weight c) Weight density d) Surface tension e) Specific gravity 2. State at least FOUR types of fluids 3. State the hydrostatic law 4. Highlight FIVE types of flow in pipes 5. List FOUR types of manometers 6. Differentiate between kinematic and dynamic viscosity and show the formulae for each of them. (4 Marks) 7. Determine the Specific gravity of a fluid having a kinematic viscosity of 0.035 stokes and a dynamic viscosity of 0.05 poise. (5 Marks) 8. Prove that the relationship between surface tension and pressure inside a droplet of a liquid in excess of outside pressure is given by the formulae: (4 Marks) alpha =(Pd)/(4) 9. State the Pascal's Law of pressure and it's SI units 10. List Three types of mechanical gauges for measuring pressure SECTION B: (60 Marks) Answer only THREE questions in this section 11. a) Prove that Kinematic Viscosity (v) is given by the formulae : (5 Marks) v=((Length)2)/(Time) b) The velocity distribution over a plate is given by (U=(2)/(5y)-y^3) in which U is the velocity in meter per second at a distance y meters above the plate Determine the shear stress at y=0M and y=0.15M Take dynamic viscosity of a fluid as 8.63 Poises. (5 Marks) (5 Marks) (4 Marks) (2 Marks) (5 Marks) (4 Marks) (3 Marks) (3 Marks)

1. Define the following terms:<br />a) Mass density: The mass per unit volume of a substance.<br />b) Specific weight: The weight per unit volume of a substance.<br />c) Weight density: The weight per unit volume of a substance.<br />d) Surface tension: The force that acts on the surface of a liquid and tends to minimize the surface area.<br />e) Specific gravity: The ratio of the density of a substance to the density of a reference substance, usually water.<br /><br />2. State at least FOUR types of fluids:<br />- Liquids<br />- Gases<br />- Plasmas<br />- Suspensions<br /><br />3. State the hydrostatic law:<br />The hydrostatic law states that the pressure exerted by a fluid in equilibrium is proportional to the depth of the fluid and the density of the fluid. Mathematically, it can be expressed as P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the fluid column.<br /><br />4. Highlight FIVE types of flow in pipes:<br />- Laminar flow<br />- Turbulent flow<br />- Transitional flow<br />- Plug flow<br />- Elastico flow<br /><br />5. List FOUR types of manometers:<br />- U-tube manometer<br />- Inverted U-tube manometer<br />- Differential manometer<br />- Mercury manometer<br /><br />6. Differentiate between kinematic and dynamic viscosity and show the formulae for each of them:<br />- Kinematic viscosity is the ratio of dynamic viscosity to the density of the fluid. It is a measure of a fluid's internal resistance to flow. The formula for kinematic viscosity is v = μ/ρ, where v is the kinematic viscosity, μ is the dynamic viscosity, and ρ is the density of the fluid.<br />- Dynamic viscosity is a measure of a fluid's resistance to flow and is independent of the fluid's density. The formula for dynamic viscosity is μ = τ/γn, where μ is the dynamic viscosity, τ is the shear stress, and γn is the normal stress.<br /><br />7. Determine the Specific gravity of a fluid having a kinematic viscosity of 0.035 stokes and a dynamic viscosity of 0.05 poise:<br />The specific gravity of a fluid can be calculated using the formula: Specific gravity = Dynamic viscosity / (Kinematic viscosity * Density of water). Given the kinematic viscosity and dynamic viscosity, we can rearrange the formula to find the density of the fluid: Density of fluid = Dynamic viscosity / Kinematic viscosity. Substituting the given values, we get: Density of fluid = 0.05 poise / 0.035 stokes = 1.43 g/cm³. Therefore, the specific gravity of the fluid is 1.43.<br /><br />8. Prove that the relationship between surface tension and pressure inside a droplet of a liquid in excess of outside pressure is given by the formulae:<br />The relationship between surface tension and pressure inside a droplet of a liquid in excess of outside pressure can be derived using the concept of equilibrium. At equilibrium, the pressure inside the droplet is equal to the pressure outside plus the pressure due to surface tension. Mathematically, this can be expressed as Pinside = Poutside + α/rd, where Pinside is the pressure inside the droplet, Poutside is the pressure outside the droplet, α is the surface tension, r is the radius of the droplet, and d is the depth of the droplet. Solving for α, we get: α = (Pinside - Poutside) * rd. Since the droplet is in equilibrium, the pressure inside is equal to the pressure at the surface, so Pinside = Poutside + α/r. Solving for α, we get: α = (Pinside - Poutside) * r. Therefore, the relationship between surface tension and pressure inside a droplet of a liquid in excess of outside pressure is given by the formulae: α = (Pinside - Poutside) * r.<br /><br />9. State the Pascal's Law of pressure and its SI units:<br />Pascal's Law states that a pressure difference applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container. The SI unit for pressure is the pascal (Pa), which is equal to one newton per square meter (N/m²).<br /><br />10. List Three types of mechanical gauges for measuring pressure:<br />- Bourdon tube gauge<br />- Diaphragm gauge<br />- Bellows gauge<br /><br />SECTION B:<br />11. a) Prove that Kinematic Viscosity (v) is given by the formulae:<br />The kinematic viscosity (v) is defined as the ratio of dynamic viscosity (μ) to the density of the fluid (ρ). Mathematically, it can be expressed as v = μ/ρ. Rearranging the formula, we get: μ = v * ρ. Therefore, the formula for kinematic viscosity is v =