A tidal estuary is dominated by the semidiurnal lunar tide,with a period of 12.42 h. If a 1 : 500 model of the estuary istested, what should be the model tidal period?( a ) 4.0 s, ( b ) 1.5 min, ( c ) 17 min, ( d ) 33 min, ( e ) 64 min
Q: Dimensional analysis with Buckinham's Pi Theorem is applied to the relationship between frictional…
A: given; head lossHf=dpdxaDbρcμdvf
Q: Applying Dimensional Analysis to the human anatomy studies, it was found that the velocity, c, at…
A:
Q: A tiny aerosol particle of density pp and characteristic diameter Dp falls in air of density p and…
A:
Q: Applying Dimensional Analysis to the human anatomy studies, it was found that the velocity, c, at…
A: It is required to perform dimensional analysis for velocity
Q: Wall friction τ w , for turbulent flow at velocity U in apipe of diameter D , was correlated, in…
A: Write the given correlation for the pipe. Here, is the wall shear stress i.e. the wall friction,…
Q: When a capillary tube of small diameter D is inserted into a container of liquid, the liquid rises…
A: Write the dimensions of the given parameters.
Q: When a steady uniform stream flows over a circular cylinder, vortices are shed at a periodic rate.…
A: Dimensions of frequency f→T-1 free stream velocity (V)= LT-1 Fluid density (ρ)=ML-3 Fluid viscosity…
Q: The radius R of a mushroom cloud generated by a nuclear bomb grows in time. We expect that R is a…
A:
Q: From Fourrier's law, the rate of heat transfer in pl. is described by: Q = S(k,A,AT, x) where k =…
A: Given Data⇒ Fourier's law of heat transfer : Q=fk,A,∆T,x We want to use Buckingham's Pi theorem to…
Q: Use the method of repeating variables to find out the non-dimensional groups for the problem of fan…
A: To find: The non dimension group . Given: The power is function of p=f(D,ρ,ω,Q). Here, P is power, D…
Q: The bending stress o in a beam depends upon the bending moment Mand the beam area moment of inertia…
A: It is required to determine dimensionally homogeneous formula for bending stress
Q: 01: Consider laminar flow over a flat plate. The boundary layer thickness 8 grows with distance x…
A: As per our Q&A guidelines we are supposed to solve only one question at once kindly repost the…
Q: A stirrer is used to mix chemicals in a large tank. The shaft power W . supplied to the stirrer…
A: Writing the dimension of the following,
Q: List the three primary purposes of dimensional analysis.
A: Dimensional Analysis is a mathematical technique that makes use of the study of dimensions as an aid…
Q: 1. Explain the three necessary conditions which must be met in order to achieve complete similarity…
A: The necessary condition which must be met in order to achieve similarity between a model and a…
Q: Ship whose full length is 100 m is to travel at 10 m/sec. For dynamical similarity, with what…
A: Given data: Lm=100 mVm=10 m/sLp=10025=4 m Need to determine the velocity.
Q: A tiny aerosol particle of density ?p and characteristic diameter Dp falls in air of density ? and…
A: The terminal setting speed (V) is a function of diameter (Dp), kinetic viscosity (μ), acceleration…
Q: A rectangular block of height Land horizontal cross-sectional area A floats at the interface between…
A: Given data as per question The density of the first fluid = p1 g/cm3 The density of second fluid =p2…
Q: An automobile has a characteristic length and area of 8 ft and 60 ft, respectively. When tested in…
A: The properties of air at sea level are: The Reynolds number is The drag coefficient is Velocity…
Q: P5.37 The volume flow Q through an orifice plate is a function of pipe diameter D, pressure drop Ap…
A:
Q: The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five…
A: Given variables are: It is given that,
Q: How can I use dimensional analysis to show that in this problem both Froude's number and Reynold's…
A:
Q: Dynamic similarity for small-scale modeling of a prototype requires, (a) a known length scale (b)…
A: from buckingham pi theorem we can get a better understanding of the relation of different parameters…
Q: Consider a boundary layer growing along a thin flat plate. This problem involves the following…
A: The boundary layer thickness depends upon the following four parameters: downstream distance, free…
Q: Consider a boundary layer growing along a thin flat plate. This problem involves the following…
A: Boundary layer thickness is the distance between the wall and bulk fluid flow and its dimension is,…
Q: The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of 5…
A:
Q: A football, meant to be thrown at 60 mi/h in sea-level air( ρ = 1.22 kg/m 3 , μ = 1.78 E-5 N ? s/m 2…
A: Given: The velocity of the prototype is VP=60 mi/h. The density of the prototype is ρ1=1.22 kg/m3.…
Q: Consider laminar flow over a flat plate. The boundary layer thickness & grows with distance x down…
A: Solution: Mathematically, boundary layer thickness can be defined as δ=f(x,U,µ,ρ), it can be written…
Q: The pressure drop AP in flow through pipes per unit length is found to depend on the average…
A:
Q: The speed of sound c in an ideal gas is known to be a function of the ratio of specific heats k,…
A: To determine: develop a functional relationship between the given parameters. There are a total of…
Q: A- The power produced from a pump (P) is fun (Hon of flow (@), pressure drop (P), Density of fluid…
A:
Q: During World War II, Sir Geoffrey Taylor, a British fluid dynamicist, used dimensional analysis to…
A: Dimension analysis is the method of establishing a relationship between different physical…
Q: The size d of droplets produced by a liquid spray nozzle isthought to depend on the nozzle diameter…
A: The given function is: O=fD,U,ρ,d,μ,γ Number of π Terms are, 6-3=3 Now taking D, U, ρ as the…
Q: A one-fiftieth-scale model of a military airplane is tested at1020 m/s in a wind tunnel at sea-level…
A:
Q: Dimensional analysis with Buckinham's Pi Theorem is applied to the relationship between frictional…
A:
Q: A prototype automobile is designed for cold weather inDenver, CO ( - 10 ° C, 83 kPa). Its drag force…
A: First assemble the necessary air density and viscosity data: Denver:…
Q: The volume flow Q through an orifice plate is a function ofpipe diameter D , pressure drop D p…
A: Q is the function of (D, ∆P, ρ, μ, d) Where, Q is the volumetric flow rate D is the pipe diameter…
Q: The drag of a sonar transducer is to be predicted, based on wind (Air) tunnel test data, The…
A:
Q: lease solve this problem, Thank you very much! Figure is attached 1. liquids in rotating cylinders…
A:
Q: The lift of a wing, Fit, is a function of wingspan, W, chord length, H, surrounding air density, p,…
A:
Q: During World War II, Sir Geoffrey Taylor, a British fl uiddynamicist, used dimensional analysis to…
A: Given data: E = f (R, ρ, t ) where R = blast wave radius , E = energy released, ρ = air density,…
Q: uniform stream overflows in a circular cylinder and then a periodic Kármán vortex street is created.…
A: Use Buckingham pi method to solve this problem
Q: The Keystone Pipeline opener photo hasD = 36 in. and an oil flow rate Q = 590,000 barrels per day(1…
A: Here, there are 5 variables and 3 primary dimensions M,L,T. Hence it is , 5-3= 2Π group. Dimensions…
Q: Famed inventor Carrie Barometer* has designed a new spherical sonar transducer for use in seawater.…
A: To determine: The number of π terms required in dimensional analysis. Given: The main variables are…
Q: (a) The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of five…
A: Since we are allowed to answer one question at a time. We’ll answer the first question since the…
Q: 2 A prototype car is designed for cold weather operation in Denver (-10°C, 83 kPa, altitude 1600m, µ…
A: Given DataTP=-10°C=263KPp=83000PaμP=1.741×10-5Pas
Q: In supersonic wind tunnel testing, if different gases areused, dynamic similarity requires that the…
A: Given Data⇒supersonic wind tunnel testingProblem definition⇒Problem says In supersonic wind tunnel…
A tidal estuary is dominated by the semidiurnal lunar tide,
with a period of 12.42 h. If a 1 : 500 model of the estuary is
tested, what should be the model tidal period?
( a ) 4.0 s, ( b ) 1.5 min, ( c ) 17 min, ( d ) 33 min, ( e ) 64 min
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
- When a steady uniform stream flows over a circular cylinder, vortices are shed at a periodic rate. These are referred to as Kármán vortices. The frequency of vortex shedding få is defined by the free-stream speed V, fluid density p, fluid viscosity u, and cylinder diameter D. Use the Buckingham Pi method to show a dimensionless relationship for Kármán vortex shedding frequency is St = f (Re). Show all your work. V DAn underwater device which is 2m long is to be moved at 4 m/sec. If a geometrically similar model 40 cm long is tested in a variable pressure wind tunnel at a speed of 60 m/sec with the following information, Poir at Standard atmospheric pressure = 1.18kg/m³ Pwater = 998kg/m3 Hair = 1.80 x 10-5 Pa-s at local atmospheric pressure and Hwater = 1 × 10-3 Pa-s then the pressure of the air in the model used times local atmospheric pressure isMott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?
- Q4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr T) and the Reynolds number %3| Vgh (Re = pch are relevant dimensionless parameters Fr = f (Re). The wave speed c of waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P.u Figure 1Q3: The power output (P) of a marine current turbine is assumed to be a function of velocity U, blade length L, angular velocity o, fluid density p and kinematic viscosity v. wL UL (a) Use dimensional analysis to show that, PU3L2 %3D (b) In a full-scale prototype the current velocity U = 2.0 m/s and the angular velocity is w = 15 rpm. A 1:10 scale laboratory model is to be tested in fluid of the same density with angular velocity o = 60 rpm. What velocity should be used in the model tests? (c) If the power output in the model tests is 200 W, what power output would be expected in the prototype?Q1) Under laminar conditions, the volume flow rate Q through a small triangular-section pore of side length (b) and length (L) is a function of viscosity (u), pressure drop per unit length (AP/L), and (b). Using dimensional analysis to rewrite this relation. How does the volume flow changes if the pore size (b) is doubled?
- 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.P1.20 A baseball, with m = 145 g, is thrown directly upward from the initial position z = 0 and Vo = 45 m/s. The air drag on the ball is CV², as in Prob. 1.19, where C~ 0.0013 N: s*/m". Set up a differential equation for the ball motion, and solve for the instantaneous velocity V(t) and position z(1). Find the maximum height zmax reached by the ball, and compare your results with the classical case of zero air drag.A2) In order to solve the dimensional analysis problem involving shallow water waves as in Figure 2, Buckingham Pi Theorem has been used. h Figure 2 Through the observation that has been done, the wave speed © of waves on the surface of a liquid is a function of the depth (h), gravitational acceleration (g), fluid density (p), and fluid viscosity (µ). By using this Buckingham Pi Theorem: a) Analyze the above problem and show that the Froude Number (Fr) and Reynolds Number (Re) are the relevant dimensionless parameters involve in this problem. b) Manipulate your Pi (1) products to get the parameter into the following form: pch := f(Re) where Re = Fr = c) If one additional primary variable parameter involve in this proolem such as, temperature (T). Discuss on the Pi (m) products that can be produce and explain why this dimensional analysis is very important in the experimental work.
- Q4: Use dimensional analysis to show that in a problem involving shallow water waves (Figure 1), both the Froude number (Fr = and the Reynolds number (Re pch. are relevant dimensionless parameters Fr = f (Re). The wave speed c of %3D waves on the surface of a liquid is a function of depth h, gravitational acceleration g, fluid density p, and fluid viscosity u. P. u Figure 1If you disturb a tank of length L and water depth h , thesurface will oscillate back and forth at frequency Ω ,assumed here to depend also upon water density ρ and theacceleration of gravity g . ( a ) Rewrite this as a dimensionlessfunction. ( b ) If a tank of water sloshes at 2.0 Hz onearth, how fast would it oscillate on Mars ( g ≈ 3.7 m/s 2 )?The Stokes number, St, used in particle dynamics studies,is a dimensionless combination of five variables: accelerationof gravity g , viscosity μ , density ρ , particle velocity U ,and particle diameter D . ( a ) If St is proportional to μand inversely proportional to g , find its form . ( b ) Showthat St is actually the quotient of two more traditionaldimensionless groups.