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Question 1
ప్రశ్న 1
For a fixed control volume, which statement correctly represents the linear momentum principle?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The control-volume momentum equation follows from Newton's second law together with the Reynolds transport theorem. The resultant external force acting on the fluid is related to both momentum stored inside the control volume and momentum transported through its boundary. For a fixed control volume, the flux contribution is evaluated as outlet momentum flux minus inlet momentum flux when one-dimensional sections are used. In steady flow the storage term vanishes, but the momentum-flux difference can still be nonzero. Therefore Option A gives the correct general interpretation.
వివరణ:
Question 2
ప్రశ్న 2
Why must the linear momentum equation normally be applied separately in the x, y and z directions?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Linear momentum is the product of mass and the velocity vector. A change in direction can therefore change momentum even when the speed remains constant. The control-volume momentum equation is consequently a vector equation. Its x, y and z components may be written and solved independently using a consistent coordinate system. Therefore Option A correctly identifies why component-wise analysis is required.
వివరణ:
Question 3
ప్రశ్న 3
A fluid particle of mass 2 kg changes velocity from 3i m/s to (-1i + 4j) m/s. What impulse acts on the particle during the change?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Impulse equals the change in linear momentum of the particle. The velocity change is (-1i + 4j) - 3i = -4i + 4j m/s. Multiplying by the mass of 2 kg gives an impulse of -8i + 8j kg·m/s. Since 1 kg·m/s is equal to 1 N·s, the result is (-8i + 8j) N·s. Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
For a control surface having outward unit normal n, which expression gives the pressure force acting on the fluid over an elemental area dA?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Pressure is a compressive normal stress. The outward unit normal points away from the control volume, whereas the pressure force exerted on the fluid acts inward. The elemental pressure-force vector is therefore -p n dA. This sign convention is particularly important at inlet and outlet sections of bends and nozzles. Hence Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
What is the purpose of the momentum correction factor β in a one-dimensional momentum calculation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The actual momentum flux through a section depends on the integral of the square of the local velocity over the area. Replacing the real velocity profile by a uniform mean velocity can therefore introduce an error. The momentum correction factor β accounts for this difference so that the momentum flux can be written in terms of the mean velocity. It is dimensionless and equals unity for a perfectly uniform velocity profile. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
Which pair of momentum correction factors β is correct for a uniform velocity profile and for fully developed laminar flow in a circular pipe, respectively?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a perfectly uniform velocity profile, every part of the section has the mean velocity and the momentum correction factor is exactly 1. Fully developed laminar flow in a circular pipe has a parabolic velocity profile. Integration of the momentum flux over that profile gives β = 4/3. This value is greater than unity because the faster central fluid contributes disproportionately to momentum flux. Therefore Option B is correct.
వివరణ:
Question 7
ప్రశ్న 7
A uniform liquid jet of area A and velocity V strikes a stationary flat plate normally and is deflected so that its outlet velocity has zero component in the original jet direction. Neglecting losses and pressure effects on the free jet, what force does the jet exert on the plate in the original jet direction?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate in the jet is ṁ = ρAV. The incoming momentum rate in the jet direction is therefore ṁV = ρAV². After striking the stationary plate, the exiting fluid is assumed to have zero velocity component in that original direction. The plate must exert a force of -ρAV² on the fluid, so the fluid exerts the equal and opposite force +ρAV² on the plate. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
A 50 mm diameter water jet moving at 20 m/s strikes a stationary flat plate normally and leaves with zero velocity component in the original jet direction. What force does the jet exert on the plate? Take ρ = 1000 kg/m³.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The jet area is A = π(0.05)²/4 = approximately 0.0019635 m². For normal impact with zero outgoing momentum component in the jet direction, the force is F = ρAV². Substitution gives F = 1000 × 0.0019635 × 20². This evaluates to approximately 785.4 N. Therefore Option C is correct.
వివరణ:
Question 9
ప్రశ్న 9
A 30 mm diameter water jet moving at 15 m/s is turned through 180 degrees by a stationary smooth cup, and its speed remains 15 m/s. What is the magnitude of the force exerted by the jet on the cup in the original jet direction? Take ρ = 1000 kg/m³.
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The jet area is π(0.03)²/4 = approximately 0.0007069 m². Reversing the velocity from +15 m/s to -15 m/s produces a velocity-component change of -30 m/s for the fluid. The magnitude of force associated with this momentum change is ṁ(30), where ṁ = ρAV. Equivalently, the force exerted by the jet on the cup is 2ρAV² = approximately 318.1 N. Therefore Option B is correct.
వివరణ:
Question 10
ప్రశ్న 10
A horizontal water jet having discharge 0.010 m³/s and speed 10 m/s enters a stationary smooth vane in the +x direction and leaves at the same speed at 60 degrees above the +x axis. Neglect pressure and weight effects. What force does the water exert on the vane?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate is ρQ = 1000 × 0.010 = 10 kg/s. The inlet velocity is 10i m/s and the outlet velocity is 10cos60° i + 10sin60° j = 5i + 8.660j m/s. The force exerted by the vane on the water is ṁ(Vout - Vin) = 10[-5i + 8.660j] = -50i + 86.6j N. By Newton's third law, the water exerts the opposite force on the vane. Therefore the required force is 50i - 86.6j N and Option A is correct.
వివరణ:
Question 11
ప్రశ్న 11
A horizontal 90-degree bend turns a water stream from the +x direction to the +y direction. The discharge is 0.050 m³/s, the mean speed is 4.0 m/s at both sections, both section pressures are zero gauge, and weight and shear forces are neglected. What force does the water exert on the bend?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The water mass-flow rate is 1000 × 0.050 = 50 kg/s. The inlet velocity is 4i m/s and the outlet velocity is 4j m/s. The bend therefore exerts on the water a force ṁ(Vout - Vin) = 50(-4i + 4j) = -200i + 200j N. Pressure, weight and shear forces have been excluded by the stated assumptions. The water exerts the equal and opposite force 200i - 200j N on the bend, so Option A is correct.
వివరణ:
Question 12
ప్రశ్న 12
A horizontal 90-degree bend turns water from +x to +y. The discharge is 0.050 m³/s, the speed is 4.0 m/s at both sections, the inlet gauge pressure is 50 kPa, the outlet gauge pressure is zero, and the inlet area is 0.0125 m². Neglect weight and wall shear. What force does the water exert on the bend?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate is 50 kg/s and the momentum-flux change is -200i + 200j N. The inlet pressure force on the control-volume fluid acts in the +x direction and equals p1A1 = 50000 × 0.0125 = 625 N. If R is the force exerted by the bend walls on the fluid, then R + 625i = -200i + 200j. Thus R = -825i + 200j N. The fluid exerts the opposite force, 825i - 200j N, on the bend, making Option A correct.
వివరణ:
Question 13
ప్రశ్న 13
A horizontal 180-degree bend carries water at 0.030 m³/s. The inlet velocity is 5i m/s and the outlet velocity is -5i m/s. Both section pressures are zero gauge and weight and shear are neglected. What force does the water exert on the bend?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate is ρQ = 1000 × 0.030 = 30 kg/s. The change in fluid velocity is -5i - 5i = -10i m/s. Therefore the bend exerts a force of 30(-10i) = -300i N on the water. There are no pressure or weight contributions under the stated assumptions. The water consequently exerts +300i N on the bend, so Option B is correct.
వివరణ:
Question 14
ప్రశ్న 14
A horizontal nozzle carries water steadily from an inlet area of 0.010 m² to an outlet area of 0.002 m² at a discharge of 0.020 m³/s. The inlet gauge pressure is 100 kPa, the outlet is a free jet at zero gauge pressure, and weight and wall shear are neglected. What force does the water exert on the nozzle in the axial direction?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Continuity gives V1 = 0.020/0.010 = 2 m/s and V2 = 0.020/0.002 = 10 m/s. The mass-flow rate is 20 kg/s, so the increase in fluid momentum rate is 20(10 - 2) = 160 N downstream. The inlet pressure force on the fluid is 100000 × 0.010 = 1000 N downstream, while the outlet gauge-pressure force is zero. The nozzle wall must therefore exert 160 - 1000 = -840 N on the fluid, meaning 840 N upstream. By Newton's third law, the water exerts 840 N downstream on the nozzle, so Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
A gas passes steadily through a device with mass-flow rate 2.0 kg/s. Its velocity increases from 50i m/s at the inlet to 150i m/s at the outlet. If pressure, gravity and shear-force contributions are negligible, what force does the gas exert on the device?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For the fluid, the momentum-flux change is ṁ(Vout - Vin). This equals 2(150 - 50)i = 200i N. Under the stated assumptions, the device must therefore exert +200i N on the gas. Newton's third law requires the gas to exert the equal and opposite force on the device. Hence the force of the gas on the device is -200i N and Option B is correct.
వివరణ:
Question 16
ప్రశ్న 16
A horizontal junction receives water at 0.060 m³/s with velocity 6i m/s. It divides equally into two outlet streams, each of discharge 0.030 m³/s and speed 6 m/s, directed at +45 degrees and -45 degrees to the +x axis. All section pressures are zero gauge and weight and shear are neglected. What resultant force does the water exert on the junction?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The inlet mass-flow rate is 60 kg/s, giving an incoming x-momentum rate of 60 × 6 = 360 N. Each outlet has mass-flow rate 30 kg/s and x-velocity 6cos45°, so their combined outgoing x-momentum rate is approximately 254.6 N. Their y-momentum components cancel because the two outlets are symmetric about the x-axis. Thus the junction exerts 254.6 - 360 = -105.4 N in the x direction on the water. The water exerts the opposite force, +105.4i N, on the junction, making Option A correct.
వివరణ:
Question 17
ప్రశ్న 17
A bend turns water from a horizontal inlet in the +x direction to a vertically upward outlet in the +y direction. The discharge is 0.010 m³/s and the speed is 5.0 m/s at both sections. Both section pressures are zero gauge, wall shear is neglected, and the water contained within the control volume weighs 100 N downward. What force does the water exert on the bend?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate is 10 kg/s. The momentum-flux change is 10[(0i + 5j) - (5i + 0j)] = -50i + 50j N. Let R be the force exerted by the bend on the water, while the fluid weight contributes -100j N. The momentum equation gives R - 100j = -50i + 50j, so R = -50i + 150j N. The water exerts the opposite force 50i - 150j N on the bend, making Option A correct.
వివరణ:
Question 18
ప్రశ్న 18
A horizontal bend changes the direction of a water stream from the +x direction to 45 degrees above the +x axis. The discharge is 0.020 m³/s and the speed is 6.0 m/s at both sections. Both section pressures are zero gauge, and weight and shear are neglected. What force does the water exert on the bend?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The mass-flow rate is 20 kg/s. The inlet velocity is 6i m/s, while the outlet velocity is 6cos45° i + 6sin45° j, or approximately 4.243i + 4.243j m/s. The bend force on the fluid is 20[(4.243 - 6)i + 4.243j] = approximately -35.1i + 84.9j N. Pressure, weight and shear contributions have been excluded by the problem statement. Therefore the water exerts approximately 35.1i - 84.9j N on the bend, so Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
For an unsteady fixed control volume, which term must be retained in the linear momentum equation in addition to the momentum flux through the control surface?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
An unsteady flow can have momentum within the control volume changing with time. The control-volume momentum equation must therefore include the time derivative of the volume integral of ρV. The momentum transported across the control surface is a separate flux contribution. In steady flow the storage term vanishes, but this simplification is not valid merely because the control volume itself is fixed. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
Which statement best distinguishes the linear momentum equation from Bernoulli's equation in typical engineering applications?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The linear momentum equation is a vector form of Newton's second law applied to a fluid system or control volume. It is especially useful for finding reactions and forces on bends, nozzles, vanes and jets because these involve changes in momentum magnitude or direction. Bernoulli's equation instead relates pressure head, velocity head and elevation head under appropriate mechanical-energy assumptions. The equations describe different conservation principles and are often used together rather than interchangeably. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
When using the momentum equation to determine the anchoring force required for a pipe bend, which procedure is most reliable?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A clear control-volume free-body analysis greatly reduces sign errors in bend-force problems. Pressure forces, body forces and wall or support reactions acting on the fluid must be included with their correct vector directions. The momentum-flux change is then evaluated independently in each coordinate direction. The calculated wall force is the force of the solid boundary on the fluid. The fluid force on the bend is equal and opposite by Newton's third law, so Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
A free water jet and the surrounding atmosphere are both at the same atmospheric pressure. When gauge pressure is used in a momentum balance around the jet, how should atmospheric pressure forces be treated?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Gauge pressure is defined relative to the surrounding atmospheric pressure. A free jet exposed to that same atmosphere therefore has zero gauge static pressure at its free boundary or discharge section under the usual approximation. Common atmospheric contributions cancel when the control-volume pressure forces are written consistently in gauge form. This simplifies jet and nozzle momentum calculations without changing the physical resultant force. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
At an inlet section of a fixed control volume, the fluid velocity is directed into the control volume while the unit normal n is defined outward. What is the sign of V·n at that inlet?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The control-surface unit normal is defined to point outward from the control volume. At an inlet, the fluid velocity points into the control volume and is therefore generally opposite to the outward normal. Their dot product V·n is consequently negative. This sign automatically makes inlet momentum flux enter the integral momentum equation with the appropriate direction. Therefore Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
A momentum calculation gives the force exerted by a pipe wall on the contained fluid as R = -400i + 150j N. What force does the fluid exert on the pipe wall?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The calculated vector R is explicitly the force of the wall on the fluid. Newton's third law states that the force of the fluid on the wall has equal magnitude and opposite direction. Reversing both components gives 400i - 150j N. This distinction is essential because engineering questions may ask either for the force on the fluid or the reaction on the fitting. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about control-volume momentum analysis: I. Momentum is a vector and must generally be resolved into components. II. Pressure forces act inward on the fluid relative to an outward control-surface normal. III. For steady one-inlet, one-outlet flow with a uniform profile, the momentum-flux contribution may be written as ṁ(Vout - Vin). IV. The force exerted by the fluid on a bend is equal and opposite to the force exerted by the bend on the fluid. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is correct because linear momentum inherits the vector nature of velocity. Statement II is correct because pressure is compressive and acts opposite to the outward surface normal. Statement III is correct for steady one-dimensional inlet and outlet sections with the stated uniform-profile assumption and consistent mass flow. Statement IV is Newton's third-law relationship between the fluid and the solid bend. Consequently all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: A. The resultant external force on the fluid equals the rate of accumulation of momentum inside the control volume plus the net outward flux of momentum across the control surface సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: A. Because momentum is a vector quantity సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. (-8i + 8j) N·s సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: B. -p n dA సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: A. It accounts for a non-uniform velocity profile when momentum flux is represented using the mean velocity సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: B. 1 and 4/3 సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: A. ρAV² సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: C. 785 N సమాధానం: C.
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Question 9 ప్రశ్న 9Answer: B. 318 N సమాధానం: B.
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Question 10 ప్రశ్న 10Answer: A. (50i - 86.6j) N సమాధానం: A.
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Question 11 ప్రశ్న 11Answer: A. (200i - 200j) N సమాధానం: A.
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Question 12 ప్రశ్న 12Answer: A. (825i - 200j) N సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: B. 300i N సమాధానం: B.
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Question 14 ప్రశ్న 14Answer: B. 840 N downstream సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: B. -200i N సమాధానం: B.
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Question 16 ప్రశ్న 16Answer: A. 105.4i N సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: A. (50i - 150j) N సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: A. (35.1i - 84.9j) N సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: A. The time rate of change of momentum stored within the control volume సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: A. The momentum equation is particularly useful for resultant force calculations involving changes in vector momentum, whereas Bernoulli's equation primarily relates mechanical-energy terms under its applicable assumptions సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: A. Isolate the fluid as a control volume, include all external forces acting on that fluid, solve for the wall force on the fluid, and then reverse its direction to obtain the fluid force on the bend సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: A. They cancel with the common atmospheric reference and the exposed jet may be taken as zero gauge pressure సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: B. Negative సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: A. 400i - 150j N సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.