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engineering
mechanical engineering
Questions and Answers of
Mechanical Engineering
The U-tube at right has a 1-cm ID and contains mercury as shown. If 20 cm3 of water is poured into the right-hand leg, what will be the free surface height in each leg after the sloshing has died
In Fig P2.23 both fluids are at 20°C. If surface tension effects are negligible, what is the density of the oil, in kg/m3?
In Prob. 1.2 we made a crude integration of atmospheric density from Table A.6 and found that the atmospheric mass is approximately m ≈ 6.08E18 kg. Can this result be used to estimate sea-level
A polytrophic atmosphere is defined by the Power-law p/po = (ρ/ρo) m, where m is an exponent of order 1.3 and po and ρo are sea-level values of pressure and density. (a) Integrate
What is the uncertainty in using pressure measurement as an altimeter? A gage on an airplane measures a local pressure of 54 kPa with an uncertainty of 3 kPa. The lapse rate is 0.006 K/m with an
A mercury manometer is connected at two points to a horizontal 20ーC water pipe flow. If the manometer reading is h 35 cm, what is the pressure drop between the two points?
Show that, for an adiabatic atmosphere, p = C(ρ)k, where C is constant, that p/po = [1−(k - 1)gz / kRT o ] k/(k-1) where k = cp/cv Compare this formula for air at 5 km altitude with the
In Fig P2.31 determine Δp between points A and B. All fluids are at 20°C.
For the manometer of Fig P2.32, all fluids are at 20°C. If pB − pA = 97 kPa, determine the height H in centimeters.
To show the effect of manometer dimensions, consider Fig. P2.34. The containers (a) and (b) are cylindrical and are such that pa = pb as shown. Suppose the oil-water interface on the right moves up a
To show the effect of manometer dimensions, consider Fig. P2.34. The containers (a) and (b) are cylindrical and are such that pa = pb as shown. Suppose the oil-water interface on the right moves up a
In Fig P2.33 the pressure at point A is 25 psi. All fluids are at 20ーC. What is the air pressure in the closed chamber B?
Water flows upward in a pipe slanted at 30°, as in Fig. P2.35. The mercury manometer reads h = 12 cm. What is the pressure difference between points (1) and (2) in the pipe?
In Fig. P2.36 both the tank and the slanted tube are open to the atmosphere. If L =2.13 m, what is the angle of tilt φ of the tube?
The inclined manometer in Fig P2.37 contains Merriam red oil, SG = 0.827. Assume the reservoir is very large. If the inclined arm has graduations 1 inch apart, what should θ be if each
In the figure at right, new tubing contains gas whose density is greater than the outside air. For the dimensions shown,(a) Find p1 (gage).(b) Find the error caused by assuming ρtube = ρair.
In Fig P2.39 the right leg of the manometer is open to the atmosphere. Find the gage pressure, in Pa, in the air gap in the tank. Neglect surface tension.
In Fig P2.40 the pressures at A and B are the same, 100 kPa. If water is introduced at A to increase pA to 130 kPa, find and sketch the new positions of the mercury menisci. The connecting tube is a
The system in Fig P2.41 is at 20°C. Determine the pressure at point A in pounds per square foot.
Small pressure differences can be measured by the two-fluid manometer in Fig. P2.42, where ρ2 is only slightly larger than ρ1, Derive a formula for pA − pB if the reservoirs are very
The traditional method of measuring blood pressure uses a sphygmomanometer, first recording the highest (systolic) and then the lowest (diastolic) pressure from which flowing “Korotkoff” sounds
Water flows downward in a pipe at 45°, as shown in Fig. P2.44. The mercury manometer reads a 6-in height. The pressure drop p2 − p1 is partly due to friction and partly due to gravity.
Determine the gage pressure at point A in Fig. P2.45, in pascals, Is it higher or lower than Patmosphere?
The cylindrical tank in Fig P2.47 is being filled with 20oC water by a pump developing an exit pressure of 175 kPa. At the instant shown, the air pressure is 110 kPa and H = 35 cm. The pump stops
In Fig P2.46 both ends of the manometer are open to the atmosphere. Estimate the specific gravity of fluid X.
Conduct an experiment: Place a thin wooden ruler on a table with a 40% overhang, as shown. Cover it with 2 full-size sheets of newspaper.(a) Estimate the total force on top of the newspaper due to
An inclined manometer, similar in concept to Fig P2.37 has a vertical cylinder reservoir whose cross-sectional area is 35 times that of the tube. The fluid is ethylene glycol at 20°C. If θ
A vat filled with oil (SG = 0.85) is 7 m long and 3 m deep and has a trapezoidal Cross-section 2 m wide at the bottom and 4 m wide at the top, as shown in Fig P2.50 Compute (a) the weight of oil in
Gate AB in Fig P2.51 is 1.2 m long and 0.8 m into the paper. Neglecting atmospheric-pressure effects, compute the force F on the gate and its center of pressure position X.
A vertical lock gate is 4 m wide and separates 20°C water levels of 2 m and 3 m, respectively. Find the moment about the bottom required to keep the gate stationary.
Panel ABC in the slanted side of a water tank (shown at right) is an isosceles triangle with vertex at A and base BC = 2 m. Find the water force on the panel and its line of action.
In Fig P2.54, the hydrostatic force F is the same on the bottom of all three containers, even though the weights of liquid above are quite different. The three bottom shapes and the fluids are the
Gate AB in Fig P2.55 is 5 ft wide into the paper, hinged at A, and restrained by a stop at B. Computea) The force on stop B; and(b) The reactions at A if h = 9.5 ft.
The tank in Fig P2.57 is 2 m wide into the paper. Neglecting atmospheric pressure, find the resultant hydrostatic force on panel BC,(a) From a single formula;(b) By computing horizontal and vertical
In Fig P2.58, weightless cover gate AB closes a circular opening 80 cm in diameter when weighed down by the 200-kg mass shown. What water level h will dislodge the gate?
The pressure in the air gap is 8000 Pa gage. The tank is cylindrical.Calculate the net hydrostatic force(a) On the bottom of the tank;(b) On the cylindrical sidewall CC; and(c) On the annular plane
Gate AB has length L, width b into the paper, is hinged at B, and has negligible weight. The liquid level h remains at the top of the gate for any angle θ. Find an analytic expression for the
For the gate of Prob. 2.55 above, stop “B” breaks if the force on it equals 9200 lbf. For what water depth h is this condition reached?
Gate AB in Fig P2.61 is a homogeneous mass of 180 kg, 1.2 m wide into the paper, resting on smooth bottom B. All fluids are at 20°C. For what water depth h will the force at point B be zero?
Gate AB in Fig P2.62 is 15 ft long and 8 ft wide into the paper, hinged at B with a stop at A. The gate is 1-in-thick steel, SG = 7.85. Compute the 20°C water level h for which the gate will
Gate ABC in Fig. P2.64 has a fixed hinge at B and is 2 m wide into the paper. If the water level is high enough, the gate will open. Compute the depth h for which this happens.
The tank in Fig P2.63 has a 4-cmdiameter plug which will pop out if the hydrostatic force on it reaches 25 N. For 20°C fluids, what will be the reading h on the manometer when this happens?
Gate AB in Fig P2.65 is semicircular, hinged at B, and held by a horizontal force P at point A. Determine the required force P for equilibrium.
Dam ABC in Fig. P2.66 is 30 m wide into the paper and is concrete (SG ≈ 2.40). Find the hydrostatic force on surface AB and its moment about C. Could this force tip the dam over? Would fluid
Isosceles triangle gate AB in Fig. P2.68 is hinged at A and weighs 1500 N. What horizontal force P is required at point B for equilibrium?
Panel BCD is semicircular and line BC is 8 cm below the surface. Determine(a) The hydrostatic force on the panel; and(b) The moment of this force about D.
Generalize Prob. 2.66 with length AB as H, length BC as L, and angle ABC as q, with width b into the
In Fig P2.71 gate AB is 3 m wide into the paper and is connected by a rod and pulley to a concrete sphere (SG = 2.40). What sphere diameter is just right to close the gate?
The cylindrical tank in Fig P2.70 has a 35-cm-high cylindrical insert in the bottom. The pressure at point B is 156 kPa. Find(a) The pressure in the air space; and(b) The force on the top of the
Weightless gate AB is 5 ft wide into the paper and opens to let fresh water out when the ocean tide is falling. The hinge at A is 2 ft above the freshwater level. Find h when the gate opens.
Gate B is 30 cm high and 60 cm wide into the paper and hinged at the top. What is the water depth h which will first cause the gate to open?
Find the height H in Fig. P2.74 for which the hydrostatic force on the rectangular panel is the same as the force on the semicircular panel below, Find
Gate AB in the figure is hinged at A, has width b into the paper, and makes smooth contact at B. The gate has density ρS and uniform thickness t. For what gate density, expressed as a function of
Panel BC in Fig P2.76 is circular. Compute(a) The hydrostatic force of the water on the panel;(b) Its center of pressure; and(c) The moment of this force about point B.
Circular gate ABC is hinged at B. Compute the force just sufficient to keep the gate from opening when h = 8 m. Neglect atmospheric pressure.
Gate ABC in Fig. P2.79 is 1-msquare and hinged at B. It opens automatically when the water level is high enough. Neglecting atmospheric pressure, determine the lowest level h for which the gate will
Analyze Prob. 2.77 for arbitrary depth h and gate radius R and derive a formula for the opening force P. Is there anything unusual about your solution?
For the closed tank of Fig P2.80, all fluids are at 20°C and the air space is pressurized. If the outward net hydrostatic force on the 40-cm by 30-cm panel at the bottom is 8450 N, estimate(a)
Gate AB is 7 ft into the paper and weighs 3000 lbf when submerged. It is hinged at B and rests against a smooth wall at A. Find the water level h which will just cause the gate to open.
The dam in Fig P2.82 is a quartercircle 50 m wide into the paper. Determine the horizontal and vertical components of hydrostatic force against the dam and the point CP where the resultant strikes
Gate AB is a quarter-circle 10 ft wide and hinged at B. Find the force F just sufficient to keep the gate from opening. The gate is uniform and weighs 3000 lbf.
Compute the horizontal and vertical components of the hydrostatic force on the quarter-circle panel at the bottom of the water tank in Fig. P2.85
Determine (a) The total hydrostatic force on curved surface AB in Fig. P2.84 and (b) Its line of action. Neglect atmospheric pressure and assume unit width into the paper.
The quarter circle gate BC in Fig. P2.86 is hinged at C. Find the horizontal force P required to hold the gate stationary. The width b into the paper is 3 m.
The bottle of champagne (SG 0.96) in Fig P2.87 is under pressure as shown by the mercury manometer reading. Compute the net force on the 2-in-radius hemispherical end cap at the bottom of the
Circular-arc Tainter gate ABC pivots about point O. For the position shown, determine (a) the hydrostatic force on the gate (per meter of width into the paper); and(b) its line of action. Does the
The tank in the figure contains benzene and is pressurized to 200 kPa (gage) in the air gap. Determine the vertical hydrostatic force on circular-arc section AB and its line of action.
A 1-ft-diameter hole in the bottom of the tank in Fig P2.90 is closed by a 45° conical plug. Neglecting plug weight, compute the force F required keeping the plug in the hole.
The hemispherical dome in Fig P2.91 weighs 30 kN and is filled with water and attached to the floor by six equally spaced bolts. What is the force in each bolt required to hold the dome down?
A 4-m-diameter water tank consists of two half-cylinders, each weighing 4.5 kN/m, bolted together as in Fig. P2.92. If the end caps are neglected compute the force in each bolt.
In Fig P2.93 a one-quadrant spherical shell of radius R is submerged in liquid of specific weight γ and depth h > R. Derive an analytic expression for the hydrodynamic force F on the shell and
The 4-ft-diameter log (SG 0.80) in Fig P2.94 is 8 ft long into the paper and dams water as shown. Compute the net vertical and horizontal reactions at point C.
The uniform body A in the figure has width b into the paper and is in static equilibrium when pivoted about hinge O. What is the specific gravity of this body when (a) h = 0; and (b) h = R?
Curved panel BC is a 60ーarc, perpendicular to the bottom at C. If the panel is 4 m wide into the paper, estimate the resultant hydrostatic force of the water on the panel.
Gate AB is a 3/8th circle, 3 m wide into the paper, hinged at B and resting on a smooth wall at A. Compute the reaction forces at A and B.
Gate ABC in Fig. P2.98 is a quarter circle 8 ft wide into the paper. Compute the horizontal and vertical hydrostatic forces on the gate and the line of action of the resultant force?
A 2-ft-diam sphere weighing 400 kbf closes the 1-ft-diam hole in the tank bottom. Find the force F to dislodge the sphere from the hole.
Pressurized water fills the tank in Fig. P2.100. Compute the hydrostatic force on the conical surface ABC.
A fuel tank has an elliptical cross-section as shown, with gasoline in the (vented) top and water in the bottom half. Estimate the total hydrostatic force on the flat end panel of the tank. The major
A cubical tank is 3 × 3 × 3 m and is layered with 1 meter of fluid of specific gravity 1.0, 1 meter of fluid with SG = 0.9, and 1 meter of fluid with SG = 0.8. Neglect atmospheric pressure. Find
A solid block, of specific gravity 0.9, floats such that 75% of its volume is in water and 25% of its volume is in fluid X, which is layered above the water. What is the specific gravity of fluid X?
The can in Fig P2.104 floats in the position shown. What is its weight in newtons?
Archimedes, when asked by King Hiero if the new crown was pure gold (SG 19.3), found the crown weight in air to be 11.8 N and in water to be 10.9 N. Was it gold?
A spherical helium balloon is 2.5 m in diameter and has a total mass of 6.7 kg. When released into the U. S. Standard Atmosphere, at what altitude will it settle?
Repeat Prob. 2.62 assuming that the 10,000 lbf weight is aluminum (SG 2.71) and is hanging submerged in the water.
A yellow pine rod (SG = 0.65) is 5 cm by 5 cm by 2.2 m long. How much lead (SG = 11.4) is needed at one end so that the rod will float vertically with 30 cm out of the water?
The float level h of a hydrometer is a measure of the specific gravity of the liquid. For stem diameter D and total weight W, if h = 0 represents SG = 1.0, derive a formula for h as a function of W,
An average table tennis ball has a diameter of 3.81 cm and a mass of 2.6 gm. Estimate the (small) depth h at which the ball will float in water at 20°C and sea level standard air if air buoyancy
A hot-air balloon must support its own weight plus a person for a total weight of 1300 N. The balloon material has a mass of 60 g/m2. Ambient air is at 25°C and 1 atm. The hot air inside the
The uniform 5-m-long wooden rod in the figure is tied to the bottom by a string. Determine (a) the string tension; and (b) the specific gravity of the wood. Is it also possible to determine the
A spar buoy is a rod weighted to float vertically, as in Fig. P2.113. Let the buoy be maple wood (SG 0.6), 2 in by 2 in by 10 ft, floating in seawater (SG 1.025). How
The uniform rod in the figure is hinged at B and in static equilibrium when 2 kg of lead (SG = 11.4) are attached at its end. What is the specific gravity of the rod material? What is peculiar about
The 2 inch by 2 inch by 12 ft spar buoy from Fig P2.113 has 5 lbm of steel attached and has gone aground on a rock. If the rock exerts no moments on the spar, compute the angle of inclination θ.
The balloon in the figure is filled with helium and pressurized to 135 kPa and 20°C. The balloon material has a mass of 85 g/m2. Estimate (a) The tension in the mooring line, and (b) The height
When the 12-cm cube in the figure is immersed in 20°C ethanol, it is balanced on the beam scale by a 2-kg mass. What is the specific gravity of the cube?
A 14-in-diameter hollow sphere of steel (SG 7.85) has 0.16 in wall thickness. How high will this sphere float in 20ーC water? How much weight must be added inside to make the
The balloon in the figure is filled with helium and pressurized to 135 kPa and 20ーC. The balloon material has a mass of 85 g/m2. Estimate (a) The tension in the mooring line, and (b) The
With a 5-lbf-weight placed at one end, the uniform wooden beam in the figure floats at an angle θ with its upper right corner at the surface. Determine(a) θ;(b) γwood
A uniform wooden beam (SG =0.65) is 10 cm by 10 cm by 3 m and hinged at A. At what angle will the beam float in 20°C water?
The uniform beam in the figure is of size L by h by b, with bah
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