1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advancethrough the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure2, and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficientdepends. In other wordsCT =FrpV2D²= fen (T₁, T₂, ...Tk)What is k? Explain.Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V.

Thrust of marine propeller = Water density = Propeller diameter = DSpeed = VAcceleration due to…

1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller , the water pressure p., and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT= pV² D² = ƒœn (T1, T², ...TH) (1) What is k? Explain. (b) Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V².

1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller , the water pressure p., and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT= pV² D² = ƒœn (T1, T², ...TH) (1) What is k? Explain. (b) Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V².

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.18P: The drag on an airplane wing in flight is known to be a function of the density of air (), the...

See similar textbooks

Similar questions

The drag on an airplane wing in flight is known to be a function of the density of air (), the viscosity of air(), the free-stream velocity (U), a characteristic dimension of the wing (s), and the shear stress on the surface of the wing (s). Show that the dimensionless drag, sU2, can be expressed as a function of the Reynolds number, Us.
Under a laminar flow, the liquid flows through small holes. It has a triangular cross-section, width b and length L, where the volumetric flow rate Q of the flow is a function of viscosity. ,pressure reduction per unit length p/L and width b 1) Use the PI theory to write the relationship as a dimensionless variable. 2) if the width b is doubled by viscosity And the pressure drop per unit length p/L is the same. I want to know how the flow rate Q will change.
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.
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/m3
The 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.
Volumetric flow rate, Q, of a pump is a function of impeller diameter d, fluid velocity V,pressure difference P, fluid density  and viscosity .a) (15P) Determine dimensionless  groups.b) (20P) A test is to be performed for a large pump that delivers 1.5 m3/s of water from 40 cmdiameter impeller with pressure rise of 400 kPa. For the test, a model with an 8 cm diameter impelleris to be used. What flow rate should be used and what would be the pressure rise in model pump
Problem statement : A simple flow-measurement device for streams and channels is a notch, of angle α, cut into the side of a dam, as shown in Fig. P5.69. The volume flow Q depends only on α, the acceleration of gravity g, and the height δ of the upstream water surface above the notch vertex. Tests of a model notch, of angle α = 55°, yield the following flow rate data: δ, cm: 10 20 30 40 Q, m3/h: 8 47 126 263 Part (A) - Find a dimensionless correlation for the data. (b) Use the model data to predict the flow rate of a prototype notch, also of angle α = 55°, when the upstream height δ is 3.2 m.
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?
The Stokes number, St, used in particle-dynamics studies is a dimensionless combination of 5 variables: acceleration of gravity g, viscosity μ, density p, particle velocity U, and particle diameter D. If St is propotional to μ and inversely proportional to g, find its dimensionless form.
Measurements at a certain point of a pipe have been done where the following parameters were recorded: Fluid of density = 887 kg/m3, Fluid velocity = 4 m/s, Pressure= 11.3 KN/m2 If the total energy per unit weight at this point = 32 m, then the potential energy is:
When 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)
The pressure difference ∆p produced by a water pump, and the power P required to operate it, each depend on the size of the pump, measured by the diameter D of the impeller, the volume flow rate ˙q, the rate of rotation ω, the water density ρ and dynamic viscosity µ. (a) Express the non-dimensional pressure difference and power as separate functions of the other non-dimensional groups. (b) Tests on a model pump are performed at 0.5 × full scale, at a rotation rate that is 2 × the full-scale value. To achieve dynamic similarity in the model test: (i) what would the volume flow rate of the water need to be in the model test compared to the full-scale? (ii) What would the pressure difference be compared to the full scale? (iii) What would the power consumption be relative to the full scale?