Fluid Mechanics: Tutorials - Unit 3

1.         In 1:30 model of spillway, the velocity and discharge are 1.5 m/s and 2 m³/s. Find the corresponding velocity and discharge in the prototype. [8.2 m/s and 9859 m³/s]

2.         An oil of specific gravity 0.9 and viscosity 0.03 poise is to be transported at the rate of 3000 lps through a 1.5 m diameter pipe. Tests were conducted on a 15 cm diameter pipe using water at 20̊C. If the viscosity of the water at 20̊c is 0.01 poise, Find,

(i) Velocity of flow in the model        [5.09 m/s]

(ii) Rate of flow in the model             [80.9 lps]

3.         In an aeroplane model of size 1/40 of its prototype, the pressure drop is 7.5 KN/m². The model is tested in water. Find the corresponding pressure drop in the prototype. Take ρ_air= 1.24 kg/m³; ρ_water = 1000 kg/m³; µ _air= 0.00018 poise; µ _water = 0.01 poise  [(Δp) _p= 1.225 N/m²]

4.         The resistance force F of a ship is a function of its length L, velocity V, acceleration due to gravity g and fluid properties like density ρ and viscosity µ. Write this relationship in a dimensionless form. F/ρV²L² = ϕ (Fr, Re)

5.         The discharge Q over a small rectangular weir is known to depend upon the head H, weir height P, gravity g, Width of the weir L and fluid properties density ρ, dynamic viscosity µ and surface tension σ. Express the relationship between the variables in dimensionless form

Q/ g ^½ H ^5/2 = fn [P/H, L/H, µ/ H^3/2 g^1/2ρ³, σ/ ρgH²]

6.         The resistance force F of a ship is a function of its length L, velocity V, acceleration due to gravity g and the fluid properties like density ρ, viscosity µ. Prove that F/ρV²L² = ϕ (Fr, Re)

7.         Oil of density 917 kg/m³ and dynamic viscosity 0.29 PaS flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows similar? Take ρ_water = 998 kg/m³ and µ _water = 1.31 x 10^-3PaS.