FUNDAMENTALS OF FLUID MECHANICS
8th Edition
ISBN: 9781119571490
Author: GERHART
Publisher: WILEY
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Chapter 6.5, Problem 48P
To determine
The potential function
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motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine:
a) the minimum permissible diameter for aluminum shafts (1) and (2)
b) the minimum permissible diameter for steel shaft (3).
c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).
First monthly exam
Gas dynamics
Third stage
Q1/Water at 15° C flow through a 300 mm diameter riveted steel pipe, E-3 mm with a head loss of 6 m in
300 m length. Determine the flow rate in pipe. Use moody chart.
Q2/ Assume a car's exhaust system can be approximated as 14 ft long and 0.125 ft-diameter cast-iron pipe (
= 0.00085 ft) with the equivalent of (6) regular 90° flanged elbows (KL = 0.3) and a muffler. The
muffler acts as a resistor with a loss coefficient of KL= 8.5. Determine the pressure at the beginning of the
exhaust system (pl) if the flowrate is 0.10 cfs, and the exhaust has the same properties as air.(p = 1.74 ×
10-3 slug/ft³, u= 4.7 x 10-7 lb.s/ft²) Use moody chart
(1)
MIDAS
Kel=0.3
Q3/Liquid ammonia at -20°C is flowing through a 30 m long section of a 5 mm diameter copper tube(e =
1.5 × 10-6 m) at a rate of 0.15 kg/s. Determine the pressure drop and the head losses.
.μ= 2.36 × 10-4 kg/m.s)p = 665.1 kg/m³
2/Y
Y+1
2Cp
Q1/ Show that
Cda
Az x
P1
mactual
Cdf
Af
R/T₁
2pf(P1-P2-zxgxpf)
Q2/ A simple jet carburetor has to supply 5 Kg of air per minute. The air is at a pressure of 1.013 bar
and a temperature of 27 °C. Calculate the throat diameter of the choke for air flow velocity of 90 m/sec.
Take velocity coefficient to be 0.8. Assume isentropic flow and the flow to be compressible.
Quiz/ Determine the air-fuel ratio supplied at 5000 m altitude by a carburetor which is adjusted to give
an air-fuel ratio of 14:1 at sea level where air temperature is 27 °C and pressure is 1.013 bar. The
temperature of air decreases with altitude as given by the expression
The air pressure decreases with altitude as per relation h = 19200 log10 (1.013), where P is in bar. State
any assumptions made.
t = ts
P
0.0065h
Chapter 6 Solutions
FUNDAMENTALS OF FLUID MECHANICS
Ch. 6.1 - Prob. 1PCh. 6.1 - The velocity in a certain flow field is given by...Ch. 6.1 - The flow in the plane two-dimensional channel...Ch. 6.1 - The three components of velocity in a flow field...Ch. 6.1 - Determine an expression for the vorticity of the...Ch. 6.1 - According to Eq. 6.134, the x-velocity in fully...Ch. 6.1 - For a certain incompressible, two-dimensional flow...Ch. 6.1 - An incompressible viscous fluid is placed between...Ch. 6.1 - A viscous fluid is contained in the space between...Ch. 6.1 - ..Air is delivered through a constant-diameter...
Ch. 6.2 - For a certain incompressible flow field it is...Ch. 6.2 - Prob. 12PCh. 6.2 - Prob. 14PCh. 6.2 - For each of the following stream functions, with...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Prob. 17PCh. 6.2 - Prob. 18PCh. 6.2 - In a two-dimensional, incompressible flow field,...Ch. 6.2 - The stream function for an incompressible flow...Ch. 6.2 - The stream function for an incompressible,...Ch. 6.2 - Consider the incompressible, two-dimensional flow...Ch. 6.3 - A fluid with a density of 2000 kg/m3 flows...Ch. 6.3 - Prob. 24PCh. 6.3 - Prob. 25PCh. 6.4 - The stream function for a given two-dimensional...Ch. 6.4 - Prob. 27PCh. 6.4 - Prob. 28PCh. 6.4 - Prob. 29PCh. 6.4 - The velocity potential for a certain inviscid flow...Ch. 6.4 - Prob. 31PCh. 6.4 - Prob. 32PCh. 6.4 - Prob. 33PCh. 6.4 - Prob. 34PCh. 6.4 - Prob. 35PCh. 6.4 - Prob. 36PCh. 6.4 - Prob. 37PCh. 6.5 - Prob. 38PCh. 6.5 - Prob. 39PCh. 6.5 - Water flows through a two-dimensional diffuser...Ch. 6.5 - Prob. 41PCh. 6.5 - Prob. 42PCh. 6.5 - Prob. 43PCh. 6.5 - Prob. 44PCh. 6.5 - Prob. 45PCh. 6.5 - Prob. 46PCh. 6.5 - Consider the flow of a liquid of viscosity μ and...Ch. 6.5 - Prob. 48PCh. 6.5 - Show that the circulation of a free vortex for any...Ch. 6.5 - Prob. 50PCh. 6.6 - Potential flow against a flat plate (Fig. P6.51a)...Ch. 6.6 - Prob. 52PCh. 6.6 - Prob. 53PCh. 6.6 - Prob. 54PCh. 6.6 - Prob. 55PCh. 6.6 - Prob. 56PCh. 6.6 -
A 15-mph wind flows over a Quonset hut having a...Ch. 6.6 - Prob. 58PCh. 6.6 - Prob. 59PCh. 6.6 - Prob. 60PCh. 6.6 - Prob. 61PCh. 6.6 - Prob. 62PCh. 6.6 - The velocity potential for a cylinder (Fig. P6.63)...Ch. 6.6 - (See The Wide World of Fluids article titled “A...Ch. 6.6 - Prob. 65PCh. 6.6 - Air at 25 °C flows normal to the axis of an...Ch. 6.8 - Determine the shearing stress for an...Ch. 6.8 - Prob. 68PCh. 6.8 - The velocity of a fluid particle moving along a...Ch. 6.8 - “Stokes’s first problem” involves the...Ch. 6.9 - Oil (SAE 30) at 15.6 °C flows steadily between...Ch. 6.9 - Prob. 72PCh. 6.9 - Prob. 73PCh. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - (See The Wide World of Fluids article titled “10...Ch. 6.9 - The bearing shown in Fig. P6.76 consists of two...Ch. 6.9 - Prob. 77PCh. 6.9 - Prob. 78PCh. 6.9 - An incompressible, viscous fluid is placed between...Ch. 6.9 - Two immiscible, incompressible, viscous fluids...Ch. 6.9 - Prob. 81PCh. 6.9 - A viscous fluid (specific weight = 80 lb/ft3;...Ch. 6.9 - A flat block is pulled along a horizontal flat...Ch. 6.9 - A viscosity motor/pump is shown in Fig. P6.84. The...Ch. 6.9 - A vertical shaft passes through a bearing and is...Ch. 6.9 - A viscous fluid is contained between two long...Ch. 6.9 - Verify that the momentum correction factor β for...Ch. 6.9 - Verify that the kinetic energy correction factor α...Ch. 6.9 - A simple flow system to be used for steady-flow...Ch. 6.9 - (a) Show that for Poiseuille flow in a tube of...Ch. 6.9 - An infinitely long, solid, vertical cylinder of...Ch. 6.9 - We will see in Chapter 8 that the pressure drop in...Ch. 6.9 - A liquid (viscosity = 0.002 N · s/m2; density =...Ch. 6.9 - Fluid with kinematic viscosity ν flows down an...Ch. 6.9 - Blood flows at volume rate Q in a circular tube of...Ch. 6.9 - An incompressible Newtonian fluid flows steadily...Ch. 6.9 - Prob. 97PCh. 6.9 - Prob. 98PCh. 6.9 - Prob. 99PCh. 6.10 - Prob. 101PCh. 6.10 - Prob. 102PCh. 6.11 - Prob. 1LLPCh. 6.11 - Prob. 2LLPCh. 6.11 - Prob. 3LLP
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