Questions and Answers of Fox And McDonald S Introduction To Fluid Mechanics

Using the data of Table 16.2, determine the moment of inertia for a flywheel for a four-cylinder 90◦ V engine having a single crank. Use Cs = 0.012 5 and a nominal speed of 4 600 rev/min. If a
Table P16.1 lists the output torque for a one-cylinder engine running at 4 600 rev/min.(a) Find the mean output torque.(b) Determine the mass moment of inertia of an appropriate flywheel using Cs =
The constant angular velocity of the crankshaft of the two-cylinder engine (Fig. P15.29, next page) isω = 250kˆ rad/s. Determine the x and y components of the primary shaking force in terms of the
The two cranks of the two-cylinder engine (Fig.P15.28, next page) are oriented at 240◦ to each other, and the crankshaft is rotating counterclockwise with a constant angular speed ω =690 rev/min.
The crankshaft of the two-cylinder engine (Fig.P15.27, page 883) is rotating counterclockwise with a constant angular speed ω = 330 rev/min.Determine the x and y components of the primary shaking
The crankshaft of the three-cylinder engine (Fig.P15.26, next page) is rotating with a constant angular velocity ω = 50kˆ rad/s. Determine the x and y components of the primary shaking force, the
The crankshaft of the two-cylinder engine (Fig.P15.25, next page) is rotating counterclockwise with a constant angular velocity ω = θ˙ = 45 rad/s.Determine the magnitude and orientation of the
The two-cylinder engine crankshaft is rotating counterclockwise with a constant angular velocity ω = 45 rad/s. Determine the magnitude and direction of the primary shaking force in terms of crank
The constant angular velocity of the two-cylinder engine crankshaft is ω = 200 rad/s counterclockwise. Determine the x and y components of the primary shaking force acting on the crankshaft bearing
The angular speed of the continuous mass system, denoted as 2, in the simply supported bearings at A and B is a constant 360 rev/min. The forces from the system acting on the ground at bearings A and
The shaft, simply supported by bearings at A and B, has a constant speed of 300 rev/min. Using the graphic approach determine the magnitudes and orientations of the reaction forces at bearings A and
The distributed mass system, denoted as body 2, is simply supported bearings at A and B and has a constant speed of 240 rev/min. The forces from the system acting on the ground at bearings A and B
The shaft of the distributed mass system is simply supported by the bearings at A and B and has a constant speed of 550 rev/min. The reaction forces acting on the bearings at A and B are FA
Three mass particles are rigidly attached to the shaft, which is rotating with a constant angular velocity ω = 350kˆ rev/min. Determine the magnitudes and orientations of the reaction forces at the
Three mass particles are rigidly attached to a simply supported shaft that is rotating with a constant angular velocity ω = 15 rad/s. Determine the magnitudes and orientations of the bearing
The shaft is simply supported by the bearings at A and B and is rotating with a constant angular velocity ω = 75 rad/s. To dynamically balance the system, determine the magnitudes and orientations
The shaft is simply supported by the bearings at A and B and is rotating with a constant angular velocity ω = 50 rad/s. Determine the magnitudes and orientations of the correcting masses that must
The shaft is rotating with a constant angular velocity ω = 80 rad/s. For dynamic balance, determine the magnitudes and orientations of the correcting masses to be removed in planes 1 and 2 at radii
A rotor is rotating with a constant angular velocityω = 50 rad/s, and is dynamically balanced by the two correcting masses. A decision has been made to use planes 1 and 3 instead of planes 1 and
A rotor to be balanced in the field yields an amplitude of 5 at an angle of 142◦ at the left bearing and an amplitude of 3 at an angle of−22◦ at the right bearing because of unbalance.To
Repeat Problem 15.9 if masses are to be added in the two correction planes.
The shaft shown in Fig. P15.7 is to be balanced by removing masses in the two correction planes, L and R. The three masses are m1 =6 g, m2 = 7 g, nd m3 = 5 g. The dimensions are a = 25 mm, b = 300
The shaft of Problem 15.7 is to be balanced by removing weight from the two correction planes.Determine the correction masses and their orientations.Figure P15.7 a = 1 in, b = e = 8 in, c = 10 in, d
The shaft is to be balanced by placing masses in correction planes L and R. Calculate the magnitudes and orientations of the correction masses.
The rotating shaft shown in Fig. P15.5 supports two masses m1 and m2, whose weights are 4 lb and 5 lb, respectively. The dimensions are a = 2 in, b =8 in, c = 3 in, R1 = 4 in, and R2 = 3 in. Find the
Determine the bearing reactions at A and B and their orientations if the shaft speed is 100 rev/min.Figure P15.5 a = c = 300 mm, b = 600 mm, R1 = R2 =60 mm, m1 = 1 kg, and m2 = 3 kg.
If the speed of the shaft is 220 rev/min, calculate the magnitudes and orientations of the bearing reactions at A and B for the two-mass system.Figure P15.4 a = b = 250 mm, c = 50 mm, R1 = 60 mm, R2
Two weights are connected to a rotating shaft and mounted outboard of bearings A and B. If the speed of the shaft is 120 rev/min, what are the magnitudes and orientations of the bearing reactions at
Three weights are connected to a shaft that rotates in bearings at A and B. Determine the magnitudes and orientations of the bearing reactions if the speed of the shaft is 300 rev/min. Also,
Determine the bearing reactions at A and B if the speed of the shaft is 300 rev/min. Also determine the magnitude and orientation of the balancing mass if it is located at a radius of 50 mm.Figure
The four-stroke engine of Prob. 14.1 has a stroke of 66 mm and a connecting rod length of 183 mm. The mass of the rod is 0.386 kg, and the center of mass is 42 mm from the crankpin. The piston
Additional data for the engine of Prob. 14.4 are l3 = 110 mm, RG3A = 15 mm, m4 = 0.24 kg, and m3 = 0.13 kg. Make a complete force analysis of the engine, and plot a graph of the crankshaft torque
Repeat Prob. 14.8, but do the computations for the same position in the compression cycle(ωt = 656.8◦).
The engine of Prob. 14.3 uses a connecting rod 300 mm long. The masses are m3A = 0.80 kg, m3B = 0.38 kg, and m4 = 1.64 kg. Find all the bearing reactions and the crankshaft torque for one cylinder of
Make a complete force analysis of the engine of Prob. 14.5. Plot a graph of the crankshaft torque versus crank angle for 720◦ of crank rotation.
Repeat Prob. 14.5, but do the computations for the compression cycle (ωt = 660◦).
The engine of Prob. 14.1 has a connecting rod 80 mm long and a mass of 0.100 kg, with the mass center 10 mm from the crankpin end. Piston mass is 0.180 kg. Find the bearing reactions and the
A single-cylinder, two-stroke gasoline engine develops 30 kW at 4 500 rev/min. The engine has an 80-mm bore, a stroke of 70 mm, and a compression ratio of 7.0. Develop a rounded indicator diagram for
Construct an indicator diagram for a V6 four-stroke gasoline engine having a 100-mm bore, a 90-mm stroke, and a compression ratio of 8.40. The engine develops 150 kW at 4 400 rev/min. Use a
Construct a rounded indicator diagram for a four-cylinder, four-stroke gasoline engine having an 85-mm bore, a 90-mm stroke, and a compression ratio of 6.25. The operating conditions to be used are
A one-cylinder, four-stroke engine has a compression ratio of 7.6 and develops brake power of 2.25 kW at 3 000 rev/min. The crank length is 22 mm with a 60-mm bore. Develop and plot a rounded
The first critical speeds of a rotating shaft with two mass disks, obtained from three different mathematical techniques, are 150 rad/s, 152 rad/s, and 153 rad/s, respectively. The influence
The steel shaft is simply supported by two bearings at A and D. Two gears are rigidly attached to the shaft at locations B and C. Gear 1 at location B weighs 150 N, gear 2 at location C weighs 90 N,
The 72-in-long shaft is simply supported by the bearings at B and D. Flywheel 1 at location A weighs 9 lb, and flywheel 2 at location C weighs 16 lb. The weight of the shaft can be neglected. The
A shaft with negligible mass is simply supported by two bearings. When a gear with a mass of 7 kg is attached to the shaft at location 1, the first critical speed is measured as 1 200 rad/s. After a
The shaft is simply supported by the bearings at A and D. Flywheel 1 at location B weighs 5.6 lb, flywheel 2 at location C weighs 17.9 lb, and the weight of the shaft can be neglected. The influence
The first and second critical speeds of a rotating shaft supporting two identical gears, each with a mass of 6 kg, are ω1 = 500 rad/s and ω2 =1 120 rad/s, respectively. If the influence coefficient
Three identical flywheels, each weighing 19 lb, are rigidly attached to a rotating shaft.The known influence coefficients of the shaft are: a11 = 2.25 × 10−4 in/lb, a22 = 10.75 ×10−4 in/lb, a33
The 600-mm-long shaft is simply supported by the bearings at A and D. Flywheel 1 at location B weighs 30 N, and flywheel 2 at location C weighs 15 N. The weight of the shaft can be neglected.The
A shaft is simply supported at A and B and is rotating with constant angular velocity ω. Two identical flywheels C and D of unknown mass are rigidly attached to the shaft (at locations 1 and 2). The
A shaft rotating with a constant angular velocity is simply supported at A and B. Gears C and D are rigidly attached to the shaft at locations 1 and 2, respectively. The weight of gear C at location
The first and second critical speeds of a rotating shaft with two flywheels rigidly attached areω1 = 375 rad/s and ω2 = 615 rad/s. The weights of the flywheels are W1 = 65 N and W2 = 80 N and the
The weights of two masses m1 and m2 that are rigidly attached to the rotating shaft are 31.5 lb and 13.5 lb, respectively. The shaft is rotating counterclockwise with a constant angular velocityω =
The weights of two gears rigidly attached to a shaft at two different locations, denoted as 1 and 2, are W1 = 200 N and W2 = 350 N, respectively. The shaft is rotating counterclockwise with a
A steel shaft, which is 50 inches in length, is simply supported by two bearings at B and D. Flywheels 1 and 2 are attached to the shaft at A and C, respectively. The flywheel at location A weighs 15
A steel shaft is simply supported by two rolling element bearings at A and C. The length of the shaft is 0.6 m, and two flywheels are attached to the shaft at the locations B and D as shown.The
A steel shaft is simply supported by two rolling element bearings at A and B. The length of the shaft is 1.45 m, and two flywheels with weight 300 N are attached to the shaft at locations shown.One
The first critical speeds of a rotating shaft with two mass disks, obtained from three different mathematical techniques, are 110 rad/s, 112 rad/s, and 100 rad/s, respectively. (a) Which values
A 600-mm-long steel shaft is simply supported by two bearings at A and C. Flywheels 1 and 2 are attached to the shaft at locations B and D, respectively. Flywheel 1 at location B weighs 50 N,
Four vibration mounts are used to support a 450-kg machine that has a rotating unbalance of 0.35 kg ·m and runs at 300 rev/min. The vibration mounts have damping equal to 30% of critical.What must
When a 6 000-lb press is mounted upon structural-steel floor beams, it causes them to deflect 0.75 in. If the press has a reciprocating unbalance of 420 lb and it operates at a speed of 80 rev/min,
A spring-mounted mass has k = 525 kN/m, c =9 640 N · s/m, and m = 360 kg. This system is excited by a force having an amplitude of 450 N at a frequency of 4.80 Hz. Find the amplitude and phase angle
A vibrating system has a spring rate of 3 000 lb/in, a damping factor of 55 lb · s/in, and a weight of 800 lb. It is excited by a harmonically varying force F0 = 100 lb at a frequency of 435 cycles
A damped vibrating system has an undamped natural frequency of 10 Hz and a weight of 800 lb.The damping ratio is 0.15. Using the phase-plane F = 2 000 lb F = 3 000 lb F = 1 000 lb F = –1 000 lb 0
Solve Problem 13.14 using damping equal to 15%of critical.
A vibrating system has k = 300 lb/in, W =90 lb, and damping equal to 20% of critical.(a) What is the damped natural frequency ωd of the system? (b) What are the period and the logarithmic decrement?
A vibrating system has a spring scale of k = 3.5 kN/m and a mass m = 15 kg. When disturbed, it is observed that the amplitude decays to one-fourth of its original value in 4.80 s. Find the damping
What is the value of the coefficient of critical damping for a spring-mass-damper system in which k = 56 kN/m and m = 40 kg? If the actual damping is 20% of critical, what is the natural frequency of
A vibrating system has a spring rate of k = 400 lb/in and a weight of W = 80 lb. Plot the response of this system to the given forcing function using:(a) three steps, and (b) six steps.F 0 0.10 t, s
An undamped vibrating system has a spring scale of 200 lb/in and a weight of 50 lb. Find the response and the final amplitude of vibration of the system if it is acted upon by the given forcing
The weight of the mass of a vibrating system is 10 lb, and it has a natural frequency of 1 Hz. Using the phase-plane method, plot the response of the system to the given force function. What is the
A motor is connected to a flywheel by a 5/8-in diameter steel shaft 36 in long. Using the methods of this chapter, it can be demonstrated that the torsional spring rate of the shaft is 4 700
A round shaft whose torsional spring constant is kt in · lb/rad connects two wheels having mass moments of inertia I1 and I2. Show that the system is likely to vibrate torsionally with a frequency
An undamped vibrating system consists of a spring whose scale is 35 kN/m and a mass of 1.2 kg. A step force F = 50 N is exerted on the mass for 0.040 s. (a) Write the equations of motion of the
Write the differential equation for the system, and find the natural frequency. Find the response x if y is a step input of height y0. Find the relative response z = x −y to this step input.Figure
The upside-down pendulum of length l is retained by two springs connected a distance a from the pivot. The springs have been positioned such that the pendulum is in static equilibrium when it is in
Weight W = 15 lb is connected to a pivoted rod that is assumed to be weightless but rigid. A spring having a rate of k = 60 lb/in is connected to the center of the rod and holds the system in static
The vibrating system has k1 = k3 = 875 N/m, k2 = 1 750 N/m, and W = 40 N. What is the natural frequency in hertz?Figure P13.5
Weight W1 drops through distance h and collides with W2 plastic impact (a coefficient of restitution of zero). Derive the differential equation of motion of the system, and determine the amplitude of
A system like Fig. 13.5 has m = 1 kg and an equation of motion x = 20 cos(8πt −π/4) mm.Determine: (a) spring constant k; (b) static deflection δst; (c) period; (d) frequency in hertz; and(e)
Evaluate the constants of integration of the solution to the differential equation for an undamped free system, using the following sets of starting conditions: (a) x = x0, x˙ = 0; (b) x = 0, x˙ =
Derive the differential equation of motion for each system, and write the formula for the natural frequency ωn for each system.Figure P13.1
For the mechanism in the posture shown, the velocity and acceleration of input link 2 down slope EA are VA = 8 in/s and AA = 24 in/s2, respectively. The wheel, link 4, is rolling without slipping on
For the linkage in the posture shown, the kinematic coefficients of link 3 are θ3 = 0.25 rad/rad and θ3 = 0.60 rad/rad2. The angular velocity and acceleration of the input link 2 are ω2 =
For the mechanism in the posture shown, the constant angular velocity of input link 2 is ω2 =3kˆ rad/s. The free length of the linear spring attached between ground pin O1 and pin A is 20 in, and a
For the mechanism in the posture shown, a force F2 = 15 N is applied at point A on input link 2, which causes the link to move up the inclined plane with a velocity VG2 = 0.5 m/s. The first and
For the linkage in the posture shown, the angular velocity and acceleration of the input link 2 areω2 = −5kˆ rad/s and α2 = 3kˆ rad/s2, respectively, and the acceleration of the mass center of
For the elliptic trammel linkage in the posture shown, the velocity and acceleration of input link 2 are VA2 = −3ˆj m/s and AA2 = 7ˆj m/s2, respectively. The kinematic coefficients, masses, and
For the linkage in the posture shown, the angular velocity and acceleration of input link 2 areω2 = −5kˆ rad/s and α2 = 3kˆ rad/s2, respectively.The kinematic coefficients are RAO2 = −10.40
For the mechanism in the posture shown, the constant angular velocity of input link 2 is ω2 =26kˆ rad/s, and the accelerations of the centers of mass of links 3 and 5 are AG3 = −8.45ˆi
For the mechanism in the posture shown, RAO2 =68 in, the position of the mass center of block 3 is 4 in below pin A, and the kinematic coefficients Figure P12.51 RG3O2 = 200 mm, RCO2 = 350 mm, andρ3
For the mechanism in the posture shown, the pin at the center of the wheel is sliding in the slot in link 2, and wheel 3 is rolling without slipping on the ground link. The constant angular velocity
Arms 2 and 3 of the flyball governor are pivoted to block 6, which remains at the height shown but is free to rotate around the y axis. Block 7 also rotates about, and is free to slide along, the y
The differential gear train has gear 1 fixed and is driven by rotating shaft 5 at 500 rev/min in the direction shown. Gear 2 has fixed bearings constraining it to rotate about the positive y axis,
The gear-reduction unit of Problem 12.46 is running at 600 rev/min when the motor is suddenly turned off, without changing the resisting-load torque. Solve Problem 12.46 for this condition.
It frequently happens in motor-driven machinery that the greatest torque is exerted when the motor is first turned on, because of the fact that some motors are capable of delivering more starting
A planetary gear-reduction unit that utilizes seven-pitch spur gears is cut on the 20◦ full-depth system. All parts are steel with a density 0.282 lb/in3. The arm is rectangular and is 4 in wide by
Repeat Problem 12.44, but assume that the wheel rotates with link 3 radially inward. Under these conditions, is there a value for the distance, r, for which the resulting angular velocity, ω3, is
Wheel 2 is a round disk that rotates about a vertical axis, z, through its center. The wheel carries a pin, B, at a distance R from the axis of rotation of the wheel, about which link 3 is free to
If the weight of the pendulum arm, Wa, is not neglected in Problem 12.42, but is assumed to be uniformly distributed over the length, l, show that the mass moment of inertia of the wheel can be

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