5.) Kinematic variables are composed of the dimensions of length and time.
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- If the following equation is dimensionally homogeneous, find the dimensions of the physical quantity K indicated in the system of fundamental physical quantities: Length, Mass and Time. Ep -G Mm K where Ep is the gravitational potential energy (same units as the kinetic energy E mv²/2), M and m are the mass of the earth and the mass of the body, respectively, and G is the universal gravitation constant G~ 6,67 x 10-11 N m² kg²The moment of the torpedo control unit in water was tested with a 1:8 scale scale model in a water tunnel of identical properties with a speed of 20 m/s if the measured moment in the model was 14 Nm. calculate 1) Determine the velocity of the prototype using the Reynolds number analogy. 2) Find the ratio of the forces occurring in the model and prototype. Using the analogy of Euler number 3) find the moment that occurred with the prototype.When a liquid in a beaker is stired, whirlpool will form and there will be an elevation difference h, between the center of the liquid surface and the rim of the liquid surface. Apply the method of repeating variables to generate a dimensional relationship for elevation difference (h), angular velocity (@) of the whirlpool, fluid density (p). gravitational acceleration (2), and radius (R) of the container. Take o. pand R as the repeating variables.
- Pide Use Buckingham's PI Theorem to determine non-dimensional parameters in the phenomenon shown on the right (surface tension of a soap bubble). The variables involved are: R AP - pressure difference between the inside and outside R- radius of the bubble Pide Soap film surface tension (Gravity is not relevant since the soap bubble is neutrally buoyant in air)Here are these questions if I could get help with themIf a spherical storage tank holds 40,000 gallons (120,000 liters) of water,what diameter must it have?If a cylindrical storage tank has a 40-foot (12 m) diameter circular 05::=how high must it be to hold 1 million gallons (3 million liters)?If water is moving at a rate of 3.2 ft3/sec (90,000 cc/sec), how manygallons (liters) per minute is this?If the specific gravity of gold is 19.0. what is the weight of a cubic inch(cubic centimeter) of gold? A cubic foot (cubic meter)?Water X 50-mm inside diameter The volume flow rate of the system The pressure at the point "A" The pressure at the point "B" 25-mm diameter As a consultant at one of the country's leading soft drink companies, you are tasked with evaluating the system depicted to determine the following parameters using Bernoulli's Equation if the values assigned to "X" and "Y" are 3m and 0.5m respectively: i. ii. iii.
- 2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂The dynamic coefficient of viscosity m (viscosity of a fluid) is from, where v= velocity, d = distance, F = Force and A = area. Find the dimensions of m.If solving the question in 3D calculations is difficult, then use the 2D system to determine the equations of the filuid pressure. Select one: O True O False A beaker is filled with a liquid of density p1 up to a certain height. A is a point, h m downwards from the free surface of the liquid as shown. The liquid is replaced by equal volume of another liquid of density p2. If p1 > p2, how will the pressure at point A change? Free Surface Base a) remain same b) increase c) decrease d) become zero Select one: O A B O C D.
- The power P required to turn a ship will depend on its velocity V , its length L, its width B, the water density ρ and viscosity µ, the rate of turning ω, and the acceleration due to gravity g. (a) Express the non-dimensional power in terms of its dependence on the other non-dimensional groups. Show all your working. (b) It is proposed to test a model ship at 1/100th scale. What scaled velocity, kinematic viscosity, and turning rate would be required for the test to be dynamically similar? Do you foresee any possible difficulties in performing this test?What is the volume of 92.4 grams of chlorine gas that is at a temperature of 46° C and a pressure of 694 mmHg? (Chlorine, R = 62.4 L- mm Hg/mole K and MW = 70.906 g/ mol) Computation: Show your Solution A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off? (Assume that friction can be ignored.)Using the following dimensional scales x' = x/l; y' = y/l; u' = u/U; v' = v/U; p' = p/(pU²); B' = B/(pU²/1); 0 = (T-T.)/AT; Re = UL/v; Pr = v/a; Sc = v/Dab, show that the governing equations can be written in the following non-dimensional form: continuity: x-motion: y-motion: Energy: Species a: du' ax' u +3y= 0 u' du' ax' Əx' +v' du' Əy' +v'. == ay' 30 u' +v'. Əx' ƏWA ax' де dy! +v' aw A Əy' др' ax' (0²u' a²u' + + 2/12 (3²1/²/² + 0²1/²1) + Bx Reax¹² dy' = ap' -1 (2²0² + 3²1/²) + By + ay' Reax¹² dyr² 1 a²0 a²0 dyr² Re Prax¹² + 1 ResTWA +2 J²WA ax¹2 ay ¹2