O The power, W, generated by a certain windmill design depends upon its diameter, D, the air density, p, the wind velocity, V, the rotation speed, Q, and the number of blades n. By using velocity V, diameter D and density. " as the repeating variables, prove the dimensionless relationship is given by DV
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- The friction force F on a smooth sphere falling in water depends on the sphere speed V, the sphere density ρ_s and diameter D_s, the density ρ and dynamic viscosity μ of the water, gravitational acceleration g. Choose the correct repeating variables. sphere diameter, dynamic viscosity, gravitational acceleration density, gravitational acceleration, dynamic viscosity friction force, gravitational acceleration, density density, sphere speed, sphere diameter friction force, sphere speed, sphere diameterWhen using the method of repeated variables in a problem, it is determined that one of the independent Πs is given by the product between the independent variable lift force FL [N], and the repeated variables density ρ [kg/m3], velocity V [m/s], and area A [m2]. Remembering that Πs are given by the product of the primary dimensions raised to the zero power, of the type m0L0t0 T0, determine this independent Π. (the form is in the side picture)Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V, pressure difference DP, fluid density r and viscosity m. a)Determine dimensionless P groups. b)A test is to be performed for a large pump that delivers 1.5 m3 /s of water from 40 cm diameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impeller is to be used. What flow rate should be used and what would be the pressure rise in model pump. Note: The model fluid is water at same temperature as the water in the prototype.
- The population P in thousands of Tallahassee, Florida, from 2000 through 2014 can be modeled by P = 150.9ekt, where t represents the year, with t = 0 corresponding to 2000. In 2005, the population of Tallahassee was about 163,075.(a) Find the value of k. Is the population increasing or decreasing? Explain. (b) Use the model to predict the populations of Tallahassee in 2020 and 2025. Are the results reasonable? Explain. (c) According to the model, during what year will the population reach 200,000?A free-falling object such as a bungee jumper is subject to the upward force of air resistance. We assumed that this force was proportional to some power b of velocity as in FU=CdVb where FU = the upward force of air resistance [N = kg m/s2 ], Cd = drag coefficient (kg/m), and V = velocity [m/s]. An individual is suspended in a wind tunnel and the force measured for various levels of wind velocity. The result might be as listed in Table 1The thrust F of a Free propeller, either aircraft of marine, depends upon density ρ, the rotation rate n in r/s, the diameter D, and the forward velocity V. Viscous effects are slight and neglected here. Tests of a 25-cm-diameter model aircraft propeller, in a sea-level wind tunnel, yield the following thrust data at a velocity of 20 m/s : Rotation Rate, r/min____4800____6000____8000 Measured thrust, N____6.1____19____47 Use the dimensionless data to predict the thrust, in Newtons, of a similar 1.6-m-diameter prototype propeller when rotating at 3800 r/min and flying at 225 mi/h at 4000-m standard altitude.
- An airplane builder wants to build a scaled-down model of a real airplane in a 12:1 ratio in order to be able to perform tests in a wind tunnel. The real plane flies at 126 km/h, while the air speed in the tunnel where the model is located is given by V. The performances of the two will be equivalent for a value of V, in m/s, equal to Data: air viscosity η = 1.8 × 10-5 kg/(m.s) air density ρ = 1.3 kg/m3The data below is from a passenger hot air balloon. The balloon is designed to lift 10-people (80 kg each person). The balloon consists of a basket, a burner- propane tank system. It will lift up when the cold air trapped inside warms up by the burner. Density of air inside the balloon is 99°C: 0.9486 kg/m³, density of air outside balloon is 20°C (ambient): 1.2041 kg/m³, Assume the balloon is a sphere shape, volume =(4/3)pi R3 Mass (kg) Balloon Basket Burner Propane tank 113.4 kg 63.5 kg 22.7 kg 183.7 kg a) Determine the minimum diameter of the balloon that would have a total lifting force to balance the weight of balloon, basket, burner, propane tank and 10 people? b) If the balloon is converted to survey the weather, it will be filled with hydrogen gas (H2). Assume the weight of the people (800kg) is now replaced by onboard equipment, what is minimum diameter needed to keep it afloat at 18km above the surface of the earth?The speed of sound traveling through the sea is a function of temperature, salinity, and pressure. It is modeled by the function C = 1449.2 + 4.67T -0.055T² +0.00029T³ + (1.34-0.01T) (S-35) + 0.016D where C is the speed of sound (in meters per second), T is the temperature (in degrees Celsius), S is the salinity (the concentration of salts in parts per thousand, which means grams of dissolved solids per 1000 grams of water), and D is the depth below the sea surface, in meters. Calculate the following (Check attached image d3) when T = 10 °C, S = 35 parts per thousand, and D = 100 m. Explain the physical meaning of these derivatives.
- The below results are for cooling tower expirement, energy balance :energy balance of the system, that is to say, the energy taken by the air must be equal to the energy supplied by the water flow. Question : Discuss the tabulated cooling tower results... Discuss in detail format!We are using simple exponential smoothing to predictmonthly electric shaver sales at Hook’s Drug Store. At theend of October 2006, our forecast for December 2006 saleswas 40. In November 50 shavers were sold, and duringDecember 45 shavers were sold. Suppose a 0.50. At theend of December, 2006, what is our prediction for the totalnumber of shavers that will be sold during March and Aprilof 2007?Using Newton’s laws, we could show that for some pendulums, the period T is related to the length l and free-fall acceleration g by T=2pi square root of (l/g) , or T2 = (4pi2/g) * l Does one of your graphs support this relationship? Explain. (Hint: Can the term in parentheses be treated as a constant of proportionality?)