Concept explainers
A person drops 3 aluminum balls of diameters 2 mm, 4 mm and 10 mm into a tank filled with glycerin at
60.4 mm/s, respectively. The measurements are to be compared with theory using Stokes law for drag force acting on a spherical object of diameter D expressed as
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Fluid Mechanics: Fundamentals and Applications
- Engine oil at 40 C flows over a 5-m-long flat plate with a free-stream velocity of 2 m/s. Determine the drag force acting on the top side of the plate per unit width. The density and kinematic viscosity of oil at 40 C are 876 kg/m^3 and 2.458 x 10 m^-4/s respectively.arrow_forwardWhat is the most important criterion for use of the modified pressure P′ rather than the thermodynamic pressure P in a solution of the Navier–Stokes equation?arrow_forwardConsider a large dirigible (like the Goodyear blimp) with length L = 240 m, and average diameter D = 40 m moving at a speed U = 135 km/hr at high altitude where the air density is p = 0.9 kg/m³ and the dynamic viscosity is u = 1.8 x 10-5 N – s/m². Because of the large size of the blimp and its large radius of curvature the primary forces acting on it are due to shear stresses at the surface, and the entire surface area can be approximated by its layout as a flat plate. Determine the drag force acting on the dirigible due to shear stresses, and the power required for the engine.arrow_forward
- A wind turbine with two or four hollow hemispherical cups connected to a pivot is commonly used to measure wind speed. Consider a wind turbine with four 1-cm-diameter cups with a center-to-center distance of 22 cm, as shown in Fig. 1. The pivot is stuck as a result of some malfunction, and the cups stop rotating. For a wind speed of 20 m/s and air density of 1.25kg/m3, determine the maximum torque this turbine applies on the pivot.arrow_forwardAir ( density :1,2 kg /m3 viscosity : 1.5x10-5 m2 /s ) flows over a flat plate of length 2,5 m and width 1 m at a test speed of 1,5 m/s. Determine the approximate magnitude of frictional force, F . (Flat plate is totally submerged in air and both surfaces of it are of same surface quality )ANSWER: F = 0,017955 Narrow_forwardA ship 200 f t long with a wetted area of 5000 ft2 moves at 25 ft/s. Find the friction drag, assuming that the ship surface may be modeled as a flat plate, and ρ = 1.94 slugs/ft3 and ν = 1.2 × 10−5 ft2/s. What is the minimum power required to move the ship at this speed?arrow_forward
- Air (p= 1.2 kg/m³, kinematic viscosity v =1.8 + 10-5 m²/s )flows along a flat plat 3 m long and 1.5 m width with a velocity of 30 km/hr. 1)Find the distance over which the boundary layer is laminar 2) determine the friction drag force and the shear stress at location where boundary layer is laminar.arrow_forwardIf a vertical wall at temperature T, is surrounded by a fluid at temperature T, a natural convection boundary layer flow will form. For laminar flow, the momentum equation is au ди. p(u-+ v) = PB(T – T)g + µ- ди ay to be solved, along with continuity and energy, for (u, v, T) with appropriate boundary conditions. The quantity B is the thermal expansion coefficient of the fluid. Use p, g, L, and (Tw- To) to nondimensionalize this equation. Note that there is no “stream" velocity in this type of flow.arrow_forwardA 30-cm-diameter smooth ball of density Phall = 210 kg/m³ is tied to an object on the bottom of a river as shown on the right. Determine the angle 0 when the speed of the river current is a. U = 1.66 m/s b. U = 0.13 m/s c. For which velocity, the drag coefficient is lower? Explain why? 30° Take the density and viscosity of water in the river Pwater = 1000 kg/m², µwater = 0.001 kg/m's. Neglect the weight of the cable and the drag on it. 400 200 100 80 60 40 20 10 0.8 0.6 0.4 0.2 0.08 0.06 2 4 68 10- 2 4 68 2 4 68 2 4 68 102 2 4 68 103 pvd 2 4 68 10 2 4 68 10 100 10 105 Reynolds number, Drag coefficient, Cparrow_forward
- A minivan is pulled by a tow truck at 60 kph. The boxlike van is 20m long, 6m high, and 3.75m wide. Estimate the skin friction, Df, on the van's top and sides. Take the density and viscosity of air as 0.0023 kg/m3 and 0.3758x10-6 N-s/m2.arrow_forward1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?arrow_forwardThe drag equation for the Gofaster 172 is: D = 0.0003v2A. D is drag in pounds; v is airspeed in feet/second; and A is aircraft frontal area in square feet. At maximum airspeed, D = 140 lbs. How much does max airspeed INCREASE if the fuselage is narrowed such that frontal area A is reduced from 16 ft2 to 14 ft2? Give the answer in ft/sec AND mph. drag is 140 lbs. at maximum airspeed, regardless of frontal area. the question is: what is the INCREASE in max airspeed, not what is the max airspeed.arrow_forward
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