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engineering
engineering fluid mechanics

Questions and Answers of Engineering Fluid Mechanics

Water flows through a horizontal branching pipe as shown in Fig. P3.109. Determine the pressure at section (3).Figure P3.109 (3) V3 A = 0.07 m (1) V = 4 m/s P = 400 kPa A = 0.1 m (2) V2 P2=350 kPa A
The "wye" fitting shown in Fig. P.3.110 lies in a horizontal plane. The fitting splits the inlet flow into two equal parts. At section 1 , the water velocity is \(12 \mathrm{ft} / \mathrm{sec}\) and
Water flows through the branching pipe shown in Fig. P3.111. If viscous effects are negligible, determine the pressure at section (2) and the pressure at section (3).Figure P3.111 Q = 1 m/s A = 0.1 m
Water flows through the horizontal branching pipe shown in Fig. P3.112 at a rate of \(10 \mathrm{ft}^{3} / \mathrm{s}\). If viscous effects are negligible, determine the water speed at section (2),
Water flows from a large tank through a large pipe that splits into two smaller pipes as shown in Fig. P3.113. If viscous effects are negligible, determine the flowrate from the tank and the pressure
A gutter running along the side of a house is 6 in. wide and \(40 \mathrm{ft}\) long. During a hard downpour, water is \(1 \mathrm{in}\). deep in the gutter. The gutter has only one downspout, and it
Air, assumed incompressible and inviscid, flows into the outdoor cooking grill through nine holes of 0.40-in. diameter as shown in Fig. P3.115. If a flowrate of \(40 \mathrm{in.}{ }^{3} /
An air cushion vehicle is supported by forcing air into the chamber created by a skirt around the periphery of the vehicle as shown in Fig. P3.116. The air escapes through the 3-in. clearance between
Water flows from the pipe shown in Fig. P3.117 as a free jet and strikes a circular flat plate. The flow geometry shown is axisymmetrical. Determine the flowrate and the manometer reading,
A conical plug is used to regulate the airflow from the pipe shown in Fig. P3.118. The air leaves the edge of the cone with a uniform thickness of \(0.02 \mathrm{~m}\). If viscous effects are
Figure P3.119 shows two tall towers. Air at \(10{ }^{\circ} \mathrm{C}\) is blowing toward the two towers at \(V_{0}=30 \mathrm{~km} / \mathrm{hr}\). If the two towers are \(10 \mathrm{~m}\) apart
Water flows steadily from a nozzle into a large tank as shown in Fig. P3.120. The water then flows from the tank as a jet of diameter \(d\). Determine the value of \(d\) if the water level in the
A small card is placed on top of a spool as shown in Fig. P3.121. It is not possible to blow the card off the spool by blowing air through the hole in the center of the spool. The harder one blows,
Observations show that it is not possible to blow the table tennis ball from the funnel shown in Fig. P3.122a. In fact, the ball can be kept in an inverted funnel, Fig. P3.122b, by blowing through
Water flows down the sloping ramp shown in Fig. P3.123 with negligible viscous effects. The flow is uniform at sections (1) and (2). For the conditions given show that three solutions for the
Water flows in a rectangular channel that is \(2.0 \mathrm{~m}\) wide as shown in Fig. P3.124. The upstream depth is \(70 \mathrm{~mm}\). The water surface rises \(40 \mathrm{~mm}\) as it passes over
A Venturi meter with a minimum diameter of 3 in. is to be used to measure the flowrate of water through a 4 -in.-diameter pipe. Determine the pressure difference indicated by the pressure gage
Determine the flowrate through the Venturi meter shown in Fig. P3.127 if ideal conditions exist.Figure P3.127 P = 735 kPa Q + 735 APU 31 mm P = 550 kPa 19 mm y=9.1 kN/m
For what flowrate through the Venturi meter of Problem 3.127 will cavitation begin if \(p_{1}=275 \mathrm{kPa}\) gage, atmospheric pressure is \(101 \mathrm{kPa}\) (abs), and the vapor pressure is
What diameter orifice hole, \(d\), is needed if under ideal conditions the flowrate through the orifice meter of Fig. P3.129 is to be \(30 \mathrm{gal} / \mathrm{min}\) of seawater with
A weir of trapezoidal cross section is used to measure the flowrate in a channel as shown in Fig. P3.130. If the flowrate is \(Q_{0}\) when \(H=\ell / 2\), what flowrate is expected when \(H=\ell\)
The flowrate in a water channel is sometimes determined by use of a device called a Venturi flume. As shown in Fig. P3.131, this device consists simply of a bump on the bottom of the channel. If the
Water flows under the inclined sluice gate shown in Fig. P3.132. Determine the flowrate if the gate is \(8 \mathrm{ft}\) wide.Figure P3.132 6 ft 30 1.6 ft 1 ft
Water flows in a vertical pipe of \(0.15-\mathrm{m}\) diameter at a rate of \(0.2 \mathrm{~m}^{3} / \mathrm{s}\) and a pressure of \(200 \mathrm{kPa}\) at an elevation of \(25 \mathrm{~m}\).
Draw the energy line and the hydraulic grade line for the flow of Problem 3.90.Problem 3.90Water flows from a large tank as shown in Fig. P3.90. Atmospheric pressure is \(14.5 \mathrm{psia}\), and
Draw the energy line and hydraulic grade line for the flow shown in Problem 3.77.Problem 3.77Water flows steadily with negligible viscous effects through the pipe shown in Fig. P3.77. It is known
Obtain a photograph/image of a flow in which it would not be appropriate to use the Bernoulli equation. Print this photo and write a brief paragraph that describes the situation involved. Bernoulli
The following table lists typical flight speeds for two aircraft. For which of these conditions would it be reasonable to use the incompressible Bernoulli equation to study the aerodynamics
A meteorologist uses a Pitot-static tube to measure the wind speed in a tornado. Based on the damage caused by the storm, the tornado is rated as EF5 on the Enhanced Fujita Scale. This means that the
Natural gas (methane) flows from a 3-in.-diameter gas main, through a 1-in.-diameter pipe, and into the burner of a furnace at a rate of \(100 \mathrm{ft}^{3} /\) hour. Determine the pressure in the
Calculate the Reynolds numbers for the flow of water and for air through a 4-mm-diameter tube, if the mean velocity is \(3 \mathrm{~m} / \mathrm{s}\) and the temperature is \(30^{\circ} \mathrm{C}\)
SAE 30 oil at \(60^{\circ} \mathrm{F}\) flows through a 2-in.-diameter pipe with a mean velocity of \(5 \mathrm{ft} / \mathrm{s}\). Determine the value of the Reynolds number (see Example
There are many fluids that exhibit non-Newtonian behavior. For a given fluid the distinction between Newtonian and non-Newtonian behavior is usually based on measurements of shear stress and rate of
Obtain a photograph/image of a situation in which the fact that in a static fluid the pressure increases with depth is important. Print this photo and write a brief paragraph that describes the
The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{~m}\) below the surface. Assume that the salt water
A closed tank is partially filled with glycerin. If the air pressure in the tank is \(6 \mathrm{lb} / \mathrm{in} .^{2}\) and the depth of glycerin is \(10 \mathrm{ft}\), what is the pressure in
A 3-m-diameter vertical cylindrical tank is filled with water to a depth of \(11 \mathrm{~m}\). The rest of the tank is filled with air at atmospheric pressure. What is the absolute pressure at the
Blood pressure is usually given as a ratio of the maximum pressure (systolic pressure) to the minimum pressure (diastolic pressure). As shown in Video V2.3, such pressures are commonly measured with
An unknown immiscible liquid seeps into the bottom of an open oil tank. Some measurements indicate that the depth of the unknown liquid is \(1.5 \mathrm{~m}\) and the depth of the oil (specific
A 30-ft-high downspout of a house is clogged at the bottom. Find the pressure at the bottom if the downspout is filled with \(60^{\circ} \mathrm{F}\) rainwater.
How high a column of SAE 30 oil would be required to give the same pressure as \(700 \mathrm{~mm} \mathrm{Hg}\) ?
Bathyscaphes are capable of submerging to great depths in the ocean. What is the pressure at a depth of \(5 \mathrm{~km}\), assuming that seawater has a constant specific weight of \(10.1 \mathrm{kN}
The deepest known spot in the oceans is the Challenger Deep in the Mariana Trench of the Pacific Ocean and is approximately \(11,000 \mathrm{~m}\) below the surface. For a surface density of \(1030
A submarine submerges by admitting seawater \((S=1.03)\) into its ballast tanks. The amount of water admitted is controlled by air pressure, because seawater will cease to flow into the tank when the
Determine the pressure at the bottom of an open 5-m-deep tank in which a chemical process is taking place that causes the density of the liquid in the tank to vary as\[ ho=ho_{\text {surf }}
In a certain liquid at rest, measurements of the specific weight at various depths show the following variation:The depth \(h=0\) corresponds to a free surface at atmospheric pressure. Determine,
Because of elevation differences, the water pressure in the second floor of your house is lower than it is in the first floor. For tall buildings this pressure difference can become unacceptable.
Under normal conditions the temperature of the atmosphere decreases with increasing elevation. In some situations, however, a temperature inversion may exist so that the air temperature increases
Equation 2.12 provides the relationship between pressure and elevation in the atmosphere for those regions in which the temperature varies linearly with elevation. Derive this equation and verify the
Often young children drink milk \(\left(ho=1030 \mathrm{~kg} / \mathrm{m}^{3}\right)\) through a straw. Determine the maximum length of a vertical straw that a child can use to empty a milk
As shown in Fig. 2.6 for the U.S. standard atmosphere, the troposphere extends to an altitude of \(11 \mathrm{~km}\) where the pressure is \(22.6 \mathrm{kPa}\) (abs). In the next layer, called the
Pikes Peak near Denver, Colorado, has an elevation of \(14,110 \mathrm{ft}\).(a) Determine the pressure at this elevation, based on Eq. 2.12.(b) If the air is assumed to have a constant specific
Bourdon gages see Fig. 2.13 are commonly used to measure pressure. When such a gage is attached to the closed water tank of Fig. P2.27 the gage reads 5 psi. What is the absolute air pressure in the
Denver, Colorado, is called the "mile-high city" because its state capitol stands on land \(1 \mathrm{mi}\) above sea level. Assuming that the Standard Atmosphere exists, what is the pressure and
Assume that a person skiing high in the mountains at an altitude of \(15,000 \mathrm{ft}\) takes in the same volume of air with each breath as she does while walking at sea level. Determine the ratio
On a given day, a barometer at the base of the Washington Monument reads 29.97 in. of mercury. What would the barometer reading be when you carry it up to the observation deck \(500 \mathrm{ft}\)
A Bourdon pressure gage attached to the outside of a tank containing air reads \(77.0 \mathrm{psi}\) when the local atmospheric pressure is \(760 \mathrm{~mm} \mathrm{Hg}\). What will be the gage
Aneroid barometers can be used to measure changes in altitude. If a barometer reads \(30.1 \mathrm{in}\). \(\mathrm{Hg}\) at one elevation, what has been the change in altitude in meters when the
A U-tube manometer is used to check the pressure of natural gas entering a furnace. One side of the manometer is connected to the gas inlet line, and the water level in the other side open to
The Wide World of Fluids article titled "Weather, barometers, and bars,". The record low sea-level barometric pressure ever recorded is 25.8 in. of mercury. At what altitude in the standard
On the suction side of a pump, a Bourdon pressure gage reads \(40 \mathrm{kPa}\) vacuum. What is the corresponding absolute pressure if the local atmospheric pressure is \(100 \mathrm{kPa}\) (abs)?
Obtain a photograph/image of a situation in which the use of a manometer is important. Print this photo and write a brief paragraph that describes the situation involved.
For an atmospheric pressure of \(101 \mathrm{kPa}\) (abs) determine the heights of the fluid columns in barometers containing one of the following liquids:(a) mercury,(b) water, (c) ethyl alcohol.
A barometric pressure of \(29.4 \mathrm{in}\). \(\mathrm{Hg}\) corresponds to what value of atmospheric pressure in psia, and in pascals?
A U-tube manometer is connected to a closed tank containing air and water as shown in Fig. P2.37. At the closed end of the manometer the air pressure is 16 psia. Determine the reading on the pressure
The U-tube manometer shown in Fig. P2.36 has two fluids, water and oil \((S=0.80)\). Find the height difference between the free water surface and the free oil surface with no applied pressure
A mercury manometer is connected to a large reservoir of water as shown in Fig. P2.35. Determine the ratio, \(h_{w} / h_{m}\), of the distances \(h_{w}\) and \(h_{m}\) indicated in the figure.Figure
The closed tank of Fig. P. 2.34 is filled with water and is \(5 \mathrm{ft}\) long. The pressure gage on the tank reads 7 psi. Determine:(a) the height, \(h\), in the open water column,(b) the gage
The container shown in Fig. P2.38 holds \(60^{\circ} \mathrm{F}\) water and \(60^{\circ} \mathrm{F}\) air as shown. Find the absolute pressures at locations \(A, B\), and \(C\).Figure P2.38 Patm =
A closed cylindrical tank filled with water has a hemispherical dome and is connected to an inverted piping system as shown in Fig. P2.39. The liquid in the top part of the piping system has a
Two pipes are connected by a manometer as shown in Fig. P2.40. Determine the pressure difference, \(p_{\mathrm{A}}-p_{\mathrm{B}}\), between the pipes.Figure P2.40 Water A+ 0.5 m 0.6 m Gage fluid
Find the percentage difference in the readings of the two identical U-tube manometers shown in Fig. P2.41. Manometer 90 uses \(90{ }^{\circ} \mathrm{C}\) water and manometer 30 uses \(30^{\circ}
A U-tube manometer is connected to a closed tank as shown in Fig. P2.42. The air pressure in the tank is \(0.50 \mathrm{psi}\) and the liquid in the tank is oil \(\left(\gamma=54.0 \mathrm{lb} /
For the inclined-tube manometer of Fig. P2.43, the pressure in pipe \(A\) is 0.6 psi. The fluid in both pipes \(A\) and \(B\) is water, and the gage fluid in the manometer has a specific gravity of
A flowrate measuring device is installed in a horizontal pipe through which water is flowing. A U-tube manometer is connected to the pipe through pressure taps located 3 in. on either side of the
The sensitivity Sen of the micromanometer shown in Fig. P2.45 is defined as\[ S e n=\frac{H}{p_{L}-p_{R}} \]Find the sensitivity of the micromanometer in terms of the densities \(ho_{A}\) and
The cylindrical tank with hemispherical ends shown in Fig. P2.46 contains a volatile liquid and its vapor. The liquid density is \(800 \mathrm{~kg} / \mathrm{m}^{3}\), and its vapor density is
Determine the elevation difference, \(\Delta h\), between the water levels in the two open tanks shown in Fig. P2.47.Figure P2.47 1 m SG = 0.90 Water 0.4 m T
What is the specific gravity of the liquid in the left leg of the U-tube manometer shown in Fig. P2.48?Figure P2.48 100 Patm Unknown fluid 15 cm Water (S= 1) 10 cm Patm 20 cm
For the configuration shown in Fig. P2.49 what must be the value of the specific weight of the unknown fluid? Express your answer in \(\mathrm{lb} / \mathrm{ft}^{3}\).Figure P2.49 5.5 in. Open Water
The manometer shown in Fig. P2.50 has an air bubble eiter in(a) the right horizontal line (b) the left vertical leg. Find \(h_{1}-h_{2}\) for both cases if \(p_{A}=p_{B}\).Figure P2.50 PA PA = PB =
The U-tube manometer shown in Fig. P2.51 has legs that are \(1.00 \mathrm{~m}\) long. When no pressure difference is applied across the manometer, each leg has \(0.40 \mathrm{~m}\) of mercury. What
Both ends of the U-tube mercury manometer of Fig. P2.52 are initially open to the atmosphere and under standard atmospheric pressure. When the valve at the top of the right leg is open, the level of
The inverted U-tube manometer of Fig. P2.53 contains oil \((S G=0.9)\) and water as shown. The pressure differential between pipes \(A\) and \(B, p_{A}-p_{B}\), is \(-5 \mathrm{kPa}\). Determine the
An inverted U-tube manometer containing oil \((S G=0.8)\) is located between two reservoirs as shown in Fig. P2.54. The reservoir on the left, which contains carbon tetrachloride, is closed and
The sensitivity Sen of the manometer shown in Fig. P2.55 can be defined as\[ \text { Sen }=\frac{h}{p_{R}-p_{L}} \]Three manometer fluids with the listed specific gravities \(S\) are
In Fig. P2.56 pipe \(A\) contains gasoline \((S G=0.7\) ), pipe \(B\) contains oil \((S G=0.9)\), and the manometer fluid is mercury. Determine the new differential reading if the pressure in pipe
The mercury manometer of Fig. P2.57 indicates a differential reading of \(0.30 \mathrm{~m}\) when the pressure in pipe \(A\) is \(30-\mathrm{mm} \mathrm{Hg}\) vacuum. Determine the pressure in pipe
Consider the cistern manometer shown in Fig. P2.58. The scale is set up on the basis that the cistern area \(A_{1}\) is infinite. However, \(A_{1}\) is actually 50 times the internal cross-sectional
The cistern shown in Fig. P2.59 has a diameter \(D\) that is 4 times the diameter \(d\) of the inclined tube. Find the drop in the fluid level in the cistern and the pressure difference
The inclined differential manometer of Fig. P2.60 contains carbon tetrachloride. Initially the pressure differential between pipes \(A\) and \(B\), which contain a brine \((S G=1.1)\), is zero as
Determine the new differential reading along the inclined leg of the mercury manometer of Fig. P2.61, if the pressure in pipe A is decreased \(10 \mathrm{kPa}\) and the pressure in pipe \(B\) remains
A student needs to measure the air pressure inside a compressed air tank but does not have ready access to a pressure gage. Using materials already in the lab, she builds a U-tube manometer using two
Determine the ratio of areas, \(A_{1} / A_{2}\), of the two manometer legs of Fig. P2.63 if a change in pressure in pipe \(B\) of 0.5 psi gives a corresponding change of \(1 \mathrm{in}\). in the
Determine the change in the elevation of the mercury in the left leg of the manometer of Fig. P2.64 as a result of an increase in pressure of 5 psi in pipe \(A\) while the pressure in pipe \(B\)
The U-shaped tube shown in Fig. 2.65 initially contains water only. A second liquid with specific weight, \(\gamma\), less than water is placed on top of the water with no mixing occurring. Can the
An inverted hollow cylinder is pushed into the water as is shown in Fig. P2.66. Determine the distance, \(\ell\), that the water rises in the cylinder as a function of the depth, \(d\), of the lower
Obtain a photograph/image of a situation in which the hydrostatic force on a plane surface is important. Print this photo and write a brief paragraph that describes the situation involved.
The basic elements of a hydraulic press are shown in Fig. P2.68. The plunger has an area of \(1 \mathrm{in.}^{2}\), and a force, \(F_{1}\), can be applied to the plunger through a lever mechanism
The hydraulic cylinder shown in Fig. P2.69, with a 4-in.diameter piston, is advertised as being capable of providing a force of \(F=20\) tons. If the piston has a design pressure (the maximum

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