using pure water at 20°C. The velocity of the prototype in seawater (p =A 1/18 scale model of the submarine is to be tested in the water tunnel1015 kg/m³, v = 1.4x106 m²/s) is 3 m/s. Determine:a) the speed of the water in the water tunnel for dynamic similarityD) the ratio of the drag force on the model to the drag force on theprototype

given; ratio of model to prototype diameter D1D2=118at temperature(T)=200cprototype density of…

using pure water at 20°C. The velocity of the prototype in seawater (p = | A 1/18 scale model of the submarine is to be tested in the water tunnel 1015 kg/m³, v = 1.4x106 m²/s) is 3 m/s. Determine: K he speed of the water in the water tunnel for dynamic similarity D) the ratio of the drag force on the model to the drag force on the prototype

using pure water at 20°C. The velocity of the prototype in seawater (p = | A 1/18 scale model of the submarine is to be tested in the water tunnel 1015 kg/m³, v = 1.4x106 m²/s) is 3 m/s. Determine: K he speed of the water in the water tunnel for dynamic similarity D) the ratio of the drag force on the model to the drag force on the prototype

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 5.8P

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5.13 The torque due to the frictional resistance of the oil film between a rotating shaft and its bearing is found to be dependent on the force F normal to the shaft, the speed of rotation N of the shaft, the dynamic viscosity of the oil, and the shaft diameter D. Establish a correlation among these variables by using dimensional analysis.
The viscous torque T produced on a disc rotating in a liquid depends upon the characteristic dimension D, the rotational speed N, the density pand the dynamic viscosity u. a) Show that there are two non-dimensional parameters written as: T and a, PND? b) In order to predict the torque on a disc of 0.5 m of diameter which rotates in oil at 200 rpm, a model is made to a scale of 1/5. The model is rotated in water. Calculate the speed of rotation of the model necessary to simulate the rotation of the real disc. c) When the model is tested at 18.75 rpm, the torque was 0.02 N.m. Predict the torque on the full size disc at 200 rpm. Notes: For the oil: the density is 750kg/m² and the dynamic viscosity is 0.2 N.s/m². For water: the density is 1000 kg/ m² and the dynamic viscosity is 0.001 N.s/m². kg.m IN =1
Q2/ A car wheel is supposed to be travelling at a speed of 80 mile per hour in the air. A scaled model (1:4) is tested in water instead of air and is supposed to have dynamic similarity. a) Determine the model speed in water b) then find the force ratio of the model to prototype if you know that: (pair = 1.22 kg/m³, µair = 1.78 x 10- 5 N.s/m?, Pwater 998 kg/m², µwater = 0.001 N.s/m²).
An 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 is
MLT By dimensional analysis, obtain an expression for the drag force (F) on a partially submerged body moving with a relative velocity (u) in a fluid; the other variables being the linear dimension (L), surface roughness (e), fluid density (p), and gravitational acceleration (g).
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8.1. An airplane wing of 3 m chord length moves through still air at 15°C and 101.3 kPa at a speed of 320 km/h. A !:20 scale model of this wing is placed in a wind tunnel, and dynamic similarity between model and prototype is desired. (a) What velocity is necessary in a tunnel where the air has the same pressure and temperature as that in flight? (b) What velocity is necessary in a variable-density wind tunnel where absolute pressure is 1 400 kPa and temperature is 15°C? (c) At what speed must the model move through water (15°C) for dynamic similarity?
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.
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The drag force on a submarine, which is moving on the surface, is to be determined by a test on a model which is scaled down to one-twentieth of the prototype. The test is to be carried in a towing tank, where the model submarine is moved along a channel of liquid. The density and the kinematic viscosity of the seawater are 1010 kg/m³ and 1.3x10-6 m 2/s, respectively. The speed of the prototype is 2.6 m/s. Assume that F = f(V, L. g. p.), using pi-theorem and similarity principle to: a) Determine the speed at which the model should be moved in the towing tank. b) Determine the kinematic viscosity of the liquid that should be used in the towing tank.