2. A student team is to design a human-powered submarine for a design competition. The overall length of the prototype submarine is 4.85 m, and its student designers hope that it can travel fully submerged through water at 0.440 m/s. The water is freshwater (a lake) at T = 15 °C. The design team builds a one-fifth scale model to test in their university's wind tunnel, as shown in the Fig. A shield surrounds the drag balance strut so that the aerodynamic drag of the strut itself does not influence the measured drag. The air in the wind tunnel is at 25 °C and at one standard atmosphere pressure. At what air speed do they need to run the wind tunnel in order to achieve similarity? Take for water at T = 15 °C and atmospheric pressure, p = 999.1 kg/m³ and µ = 1.138 × 10³ Pa.s. Take for air at T = 25 °C and atmospheric pressure, p = 1.184 kg/m³ and μ = 1.849 × 105 Pa.s. Wind tunnel test section V Poo, P 801 Model Shield FD Drag balance Strut

A dimensional analysis is performed on the drag on a boat. When the effects of viscosity can be neglected, the Euler number based on the drag D experienced by the boat is a function of a Froude number. The effects of the dimensions of the boat can be represented by its length I. The drag on a model of the model is measured as 0.35N. If the ratio of / for a full-scale model to the value of/ for the model is 46, calculate the expected drag on the full-scale boat. Your answer should be to the nearest kN. The properties of the water in the model test matches those for the full-scale boat.

A block, as shown below, is sliding on a thin horizontal layer of water (u = 1.68 x 103 kg/m.s) between ice and the block with a speed of 13 m/s. The thickness of the water layer is 3.32 x 10-5 m. Given the following dimensions of the block, what is the force (F) required to maintain this movement? A = 9 cm B = 9 cm C= 8 cm B 2.96 N 5.33 N 4.14 N 4.74 N

1. (a) The motion of a floating vessel through the surrounding fluid results in a drag force D which is thought to depend upon the vessel's speed v, its length I, the density p and dynamic viscosity μ of the fluid and the acceleration due to gravity g. Show that:- D = pv²1² (1) (b) In order to predict the drag on a full scale 50m long ship traveling at 7m/s in sea water at 5°C of density 1027.7225 kg/m³ and viscosity 1.62 x 103 Pa.s, a model 3m long is tested in a liquid of density 805 kg/m³. What speed does the model need to be tested at and what is the required viscosity of the liquid?

1. A model submarine is tested in a sea water tank at a speed of 30 m/s. The prototype speed should be 21.6 km/hr. (a) Determine the geometric scale between the model and the prototype (b) Determine the model speed if it is tested in a pressurized air wind tunnel with 12/s. kinematic viscosity v = 8 × 10-7 m² /s. For sea water use v = 1.124 × 10-6 m² /s.

Engineers are worried about the wind forces on a sculpture in Queen Mary campus. The sculpture has a height Ha = 5 m and a diameter, Da = 2 m, as shown in Figure Q3. The engineers decide to investigate making a smaller scale model testing in a water tunnel. They need to match the Reynolds number and the aspect ratio, AR = H/D. The characteristic length scale in the Reynolds number can be the diameter. Water has a density and viscosity of pw = 1000 kg/m3 and μw = 1 mPa. s, while air has a density and viscosity of pa = 1.2 kg/m3 and μa = 18 x 10-6 Pa. s. The average wind speed by the sculpture is Ua = 6 m/s. 1. The maximum height of the model that the engineers can place in the water tunnel is 1.5 m. Find the diameter of the model needed. 2. Find the average speed of water needed for the experiments to match the average wind speed past the sculpture. 3. It is known that at a wind speed of Ua = 4 m/s, the flow past the sculpture becomes turbulent. To visualise the flow in the experiments,…

The drag on a 2-m-diameter satellite dish due to an 69-km/hr wind is to be determined through a wind tunnel test using a geometrically similar 0.4-m-diameter model dish. Assume standard air for both model and prototype. (a) At what air speed should the model test be run? (b) With all similarity conditions satisfied, the measured drag on the model was determined to be 152 N. What is the predicted drag on the prototype dish? (a) Vm = (b) D = i i km/hr N