Consider water flow around a circular cylinder, of diameter D and length l. In addition to geometry, the drag force is known to depend on liquid speed, V, density, ρ, and viscosity, μ. Express drag force, FD, in dimensionless form as a function of all relevant variables. The static pressure distribution on a circular cylinder, measured in the laboratory, can be expressed in terms of the dimensionless pressure coefficient; the lowest pressure coefficient is Cp = −2.4 at the location of the minimum static pressure on the cylinder surface. Estimate the maximum speed at which a cylinder could be towed in water at atmospheric pressure, without causing cavitation, if the onset of cavitation occurs at a cavitation number of 0.5.
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- > | E9 docs.google.com/form تبديل الحساب Questions 7 نقاط Q1/ The power of 6-blade flat blade turbine agitator in a tank is a function of diameter of impeller, number of rotations of the impeller per unit time, viscosity and density of liquid. From a dimensional analysis, obtain a relation between the power and the four variables. 3. صفحة 2 منarrow_forwardThe power P required to drive a propeller is known to depend on the diameter of the propeller D, the density of fluid ρ, the speed of sound a, the angular velocity of the propeller ω, the freestream velocity V , and the viscosity of the fluid µ. (a) How many dimensionless groups characterize this problem? (b) If the effects of viscosity are neglected, and if the speed of sound is not an important variable, express the relationship between power and the other variables in nondimensional form. (c) A one-half scale model of a propeller is built, and it uses Pm horsepower when running at a speed ωm. If the full-scale propeller in the same fluid runs at ωm/2, what is its power consumption in terms of Pm if the functional dependence found in part (b) holds? What freestream velocity should be used for the model test?arrow_forwardViscosity of fluid plays a significant role in the analyses of many fluid dynamics problems. The viscosity of water can be determined from the correlation: H = c, where µ = viscosity (N/s · m²) T = temperature (K) C, = 2.414 × 10-5 C; = 247.8 (K) Cz = 140 (K) What is the appropriate unit for c, if the preceding equation is to be homogeneous in units?arrow_forward
- 1) At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes erupt each year. Over the past 100 years, an average of 850 people have died each year from volcano eruptions. As scientists and engineers study the mechanics of lava flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives after an eruption. Jeffrey's equation captures the relationship between flow rate and viscosity as: Flow V = Pgt sin(@) 28 сm 10 where p is the density of the lava, g is gravity, t is the flow thickness, a is the slope, and u is the lava viscosity. Typical values are given as follows for the flow rate: u= 4x103 kg/(m.s) ±1% p= 2.5 g/cm³ ±1% t= 28 cm +0.5 cm a= 10° +1 ° g= 9.81 m/s? Determine the likely maximum possible error in the calculated value of the flow rate.arrow_forwardThe property of a fluid called viscosity is related to its internal friction and resistance to being deformed. The viscosity of water, for instance, is less than that of molasses and honey, just as the viscosity of light motor oil is less than that of grease. A unit used in mechanical engineering to describe viscosity is called the poise, named after the physiologist Jean Louis Poiseuille, who performed early experiments in fluid mechanics. The unit is defined by 1 poise = 0.1 (N s)/m2. Show that 1 poise is also equivalent to 1 g/(cm · s). %3Darrow_forwardQ.7. In an Aeroplan model of size 1/10 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 Density of air = 1.24 kg/m³. Density of water = 1000 kg/m³.Viscosity of air = 0.00018 poise Viscosity of water = 0.01 poisearrow_forward
- A dimensionless expression that is significant quantities in the area of viscous flow through channels is called Reynolds number, Re, defined as pDV/u where is p the fluid density, V the mean fluid velocity, D the pipe diameter, and u the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 N-s/m2 and a specific gravity of 0.91 flows through a 25-mm-diameter pipe with a velocity of 2.6 m/s. Determine the value of the Reynolds number in SI Units.arrow_forwardAn incompressible fluid oscillates harmonically (V = Vosinut, where Vis the velocity) with a frequency of 9 rad/s in a 6-in.-diameter pipe. A 1/5 scale model is to be used to determine the pressure difference per unit length, Ap, (at any instant) along the pipe. Assume that Api= f(D, Vo, w, t, u, p) where D is the pipe diameter, w the frequency, t the time, the u fluid viscosity, and p the fluid density. If the same fluid is used in the model and the prototype, at what frequency should the model operate? Wm i rad/sarrow_forwardA dimensionless combination of variables that is important in the study of viscous flow through pipes is called the Reynolds number, Re, defined as ???/? where, as indicated in Fig. 11, ? is the fluid density, V the mean fluid velocity, D the pipe diameter, and the fluid viscosity. A Newtonian fluid having a viscosity of 0.38 ? . ?/?² and a specific gravity of 0.91 flows through a 25‐mmdiameter pipe with a velocity of 2.6 ?/?. Determine the value of the Reynolds number using (a) SI units, and (b) BG units.arrow_forward
- 1ODiem # The side thrust F, for a smooth spinning ball in a fluid is a function of the ball diameter D, the free-stream velocity V, the densityp, the viscosityu, and the angular velocity of spino. F= f( D, ρ, μ, V, ω) Using the Buckingham Pi theorem to express this relation in dimensionless form. Farrow_forwardIn the development of a new piece of equipment, it is necessary to measure the shear stress (7) between two parallel plates where the lower plate is stationary and the upper plate moves at a velocity (V) of 2m/sec. The plates are 0.025m apart (h). The shear stress 7 is estimated by 2m/sec = 0.025m V 80μ. The viscosity (4) in N – sec/m² is a function of temperature. Laboratory measurements have determined µ at the temperatures shown in the table below: T(°C) | (µ)(N – sec/m² 5 0.08 20 0.015 30 0.009 50 0.006 55 0.0055arrow_forwardThe Reynolds number is a dimensionless group defined as follows for a liquid that flows through a pipe: Re = Dvρ / μ where D is the diameter of the pipe, v is the velocity of the fluid, ρ is its density and µ its viscosity. When the Reynolds number value is less than 2100, the flow is laminar, that is, the liquid it moves in lines of smooth flow. For Reynolds numbers greater than 2100, the flow is turbulent, characterized by considerable agitation. Liquid Methyl Ethyl Ketone (MEK) flows through 2067 '' ID tubing and through an average velocity of 0.48 ft / s. If the fluid temperature is 20 ° C, the density of the MEK The liquid is 0.805 g / cm and the viscosity is 0.43 cP (1 cP = 1.00 x 10 kg / (m-s)]. Determine the Reynolds number for MEK flow conditions. (Round the final result to a whole number without decimals).arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning