Hydraulics And Fluid Mechanics — Part 1 MCQs with Explanations

Understanding the Problem: We need to find the center of pressure on a rectangular surface submerged in water. The center of pressure is the point where the total hydrostatic force acts on the surface. Key Concepts: For a vertically submerged rectangle , the center of pressure (h cp ) is located below the centroid (center of area). The formula to calculate h cp is: h cp = h c + (I xx / (A * h c )) Where: h c is the depth of the centroid from the free surface. I xx is the second moment of area (moment of inertia) about the centroidal axis. A is the area of the submerged surface. Step-by-Step Solution: 1. Find the depth of the centroid (h c ): The rectangle's top is at 1.5 m and the bottom is at 6.0 m. The height of the rectangle is 6.0 m - 1.5 m = 4.5 m. The centroid is located at the middle of the rectangle's height. So, h c = 1.5 m + (4.5 m / 2) = 1.5 m + 2.25 m = 3.75 m 2. Calculate the Area (A): We are not given the width (b) of the rectangle so we consider it as b. Height of the rectangle h = 4.5 m A = b * h = b * 4.5 m 3. Calculate the Moment of Inertia (I xx ): For a rectangle about its centroidal axis, I xx = (b * h 3 ) / 12. I xx = (b * (4.5) 3 ) / 12 = (b * 91.125) / 12 4. Calculate the Center of Pressure (h cp ): h cp = h c + (I xx / (A * h c )) h cp = 3.75 + (((b * 91.125) / 12) / ((b * 4.5) * 3.75)) h cp = 3.75 + ((b * 91.125) / 12) / (b * 16.875) h cp = 3.75 + (91.125 / 12) / 16.875 (b cancels out) h cp = 3.75 + (7.59375 / 16.875) h cp = 3.75 + 0.45 h cp = 4.2 m Therefore, the correct answer is Option C: 4.2 m.

Weight (W) is the force exerted by gravity on an object and is given by the formula W = m * g Here, the mass (m) of the object is 10 kg The weight of the object as measured by the spring balance is 9.81 kg (which is actually a measure of force in newtons but given in kg for simplicity) To find the acceleration due to gravity (g) at this place, we use the formula: g = W / m Substituting the given values: g = 9.81 kg / 10 kg g = 9.81 m/sec 2 Therefore, the value of 'g' at this place is 9.81 m/sec 2

Buoyant force is the upward force exerted by a fluid on a submerged or partially submerged object. This force acts vertically upward through the center of buoyancy, which is the centroid of the displaced fluid volume. Since pressure in a fluid acts equally in all directions at a given depth , any horizontal forces acting on opposite sides of the object cancel each other out. As a result, the horizontal components of the pressure forces balance out , and only the vertical component remains as the net buoyant force. Conclusion: The horizontal component of buoyant force is zero , making Option C the correct answer.

Surface tension is a measure of force per unit length, the SI units for which is newtons per meter (N/m).

When fluid flows through a pipe, energy is lost due to friction , and this loss is called the head loss. The power transmitted by the fluid depends on the head available after accounting for this frictional loss. Let the total head supplied be H, and let the head loss due to friction be h f . Then, the head available for power transmission = H – h f Horsepower transmitted ∝ (H – h f ) × flow rate , and flow rate itself ∝ √(H – h f ) Hence, horsepower transmitted is proportional to (H – h f ) 1.5 To maximize power, differentiate the expression and solve: the power transmitted is maximum when h f = H / 3 That means, head loss due to friction is one-third of the total head supplied . Therefore, the correct answer is: Option A — 1/3

The resultant of all normal pressures in a fluid acts at the center of pressure . The center of pressure is the point where the total force due to fluid pressure can be considered to act on a submerged surface. It is essential in the analysis of fluid forces on submerged surfaces. Therefore, the correct answer is Option B: at center of pressure .

Pressures of the order of 10⁻⁷ torr (very high vacuum) are extremely low and cannot be measured by ordinary pressure-measuring devices. A Bourdon tube is used for measuring relatively high pressures and is unsuitable for vacuum measurements. A micro-manometer is used for small pressure differences but not for very high vacuum ranges. A Pirani gauge can measure low pressures only up to about 10⁻³ torr . An ionisation gauge operates on the principle of ionizing gas molecules and is specifically designed to measure very low pressures (high vacuum) of the order of 10⁻⁷ torr and below . Hence, the correct answer is ionisation gauge .

Flow measurement in large diameter pipes, such as a 3-meter diameter water pipe, requires devices that can handle high flow rates and provide accurate readings with minimal energy loss. An orifice plate causes significant head loss and is more suitable for smaller pipes. A rotameter is typically used for low flow rates and smaller pipe diameters in vertical applications. A pitot tube can measure velocity at a point but is not practical for measuring total flow in such a large pipe. The venturi meter is specifically designed to measure flow in large pipes. It operates on the principle of pressure differential and causes minimal energy loss. Therefore, for a pipe about 3 meters in diameter, the most suitable device is the venturi meter. Correct answer is Option B: venturi

In fluid mechanics, shear stress in a pipe flow is related to the velocity gradient (rate of change of velocity with respect to radial distance from the pipe wall). In laminar flow through a circular pipe, the velocity is maximum at the center and decreases toward the pipe wall. At the center line of the pipe, the velocity gradient is zero because the slope of the velocity profile flattens out at the peak. Since shear stress is directly proportional to the velocity gradient , a zero velocity gradient results in zero shear stress . Hence, the shear stress is minimum (actually zero) at the center line of the pipe. Therefore, the correct answer is: minimum (Option A).

A floating body is said to be in equilibrium when it remains stable and doesn't overturn or sink. This equilibrium is maintained by a combination of factors. The options provided outline these factors: 1. Meta center should be above e.g.: The metacenter (M) is a point above the center of buoyancy (B) in a floating body. When the metacenter is above the center of gravity (G), the body tends to return to its equilibrium position if disturbed. This stability is crucial for preventing overturning. 2. Center of buoyancy and e.g. must lie on the same vertical plane: The center of buoyancy (B) is the point where the buoyant force acts vertically upward. For equilibrium, the center of gravity (G) and center of buoyancy (B) must lie on the same vertical line. This ensures that the body doesn't tilt or rotate. 3. A righting couple should be formed: A righting couple is a moment that tends to restore a floating body to its original upright position when it is tilted. It is created by the displacement of water due to the tilt of the body. This righting couple counteracts any tendency for the body to capsize. In summary, all of the provided options contribute to the conditions required for a floating body to be in equilibrium. The metacenter's position, alignment of centers of buoyancy and gravity, and the formation of a righting couple collectively ensure the stability and equilibrium of the floating body.

In the field of hydraulics and fluid mechanics , a broad-crested weir is employed to manage water flow in open channels. This structure is pivotal for measurement and control purposes. The discharge over such a weir is contingent on the depth of flow, which is referred to as the head over the weir. Various empirical equations govern the relationship between discharge and head. Among the given options, the correct choice is Option B: $$\frac{{2H}}{3}$$ . This signifies that the discharge over a broad-crested weir reaches its maximum when the depth of flow (head) equals two-thirds of the available head (H). This specific proportion maximizes the flow rate of discharge over the weir. Therefore, the accurate answer is Option B: $$\frac{{2H}}{3}$$ .

In the context of fluid mechanics and viscosity measurement, the Orsat meter is not associated with viscosity. The Orsat meter is primarily used for the analysis of gas composition, particularly for measuring the percentage of carbon dioxide, oxygen, and other gases in a gas sample. On the other hand: Option A: Redwood viscometer is associated with measuring viscosity. Option B: Saybolt viscometer is used for measuring the viscosity of petroleum products. Option C: Engler viscometer is another instrument used for measuring viscosity. Therefore, the correct answer is Option D: Orsat , as it is not related to viscosity measurement.

Reynolds number is a very important dimensionless quantity in fluid mechanics. It helps us understand whether the flow of a fluid (like water in a pipe) is smooth (laminar) or chaotic (turbulent) . Imagine water flowing through a pipe. If the flow is laminar, it's like perfectly ordered layers of water sliding smoothly over each other. Turbulent flow, on the other hand, is messy! It involves swirling, mixing, and unpredictable changes in the water's velocity. The Reynolds number (Re) is calculated using the fluid's properties (density, viscosity), its velocity, and the pipe's diameter. A higher Reynolds number means a higher velocity or a larger diameter , leading to more chaotic flow. For flow in pipes, we use a general guideline based on the Reynolds number: - Laminar flow: Re < 2000 - Transition region (between laminar and turbulent): 2000 < Re < 4000 (the flow can be either laminar or turbulent in this range) - Turbulent flow: Re > 4000 Therefore, turbulent flow in pipes occurs when the Reynolds number is more than 4000 .

The upper surface of a weir over which water flows is called the crest. The crest is the highest point of the weir, and it controls the flow of water over the structure. The nappe refers to the sheet of water that flows over the weir crest. The sill is the bottom edge or base of the weir structure, which supports the crest. Weir top is not a technical term used in hydraulics and fluid mechanics. Thus, the correct answer is crest.

The Mach number (Ma) represents the ratio of the speed of an object (such as an aircraft) to the speed of sound in the surrounding medium. It is used to characterize compressible flows, particularly in aerodynamics. The Mach number helps determine the behavior of fluid flows at high speeds where the effects of compressibility become significant.

In fluid mechanics, when the flow parameters (like velocity, pressure, etc.) at any given instant remain constant at every point in the flow, the flow is referred to as steady. Let’s analyze the options: Option A: quasi static → Incorrect. Quasi-static refers to processes that are almost in equilibrium, but not exactly steady or unchanging. It is more related to slow, reversible processes rather than the condition where flow parameters remain constant. Option B: steady state → Correct. In steady-state flow, the velocity and other flow parameters do not change with time at any given point in the fluid. This means that the flow is time-independent at every location. Option C: laminar → Incorrect. Laminar flow refers to a flow regime where fluid moves smoothly in layers, without turbulence. However, laminar flow does not necessarily imply that the flow parameters are constant at every point in time. Option D: uniform → Incorrect. Uniform flow means the flow parameters are the same throughout the entire flow field at any given instant, but it does not specifically imply that these parameters remain constant over time. It only implies spatial uniformity, not temporal steadiness. Thus, the correct answer is Option B: steady state , as it describes the condition where flow parameters remain the same at every point, with no change over time.

Viscosity is a measure of a fluid's resistance to flow. It is affected by temperature differently for liquids and gases. Effect of Temperature on Liquids: - As temperature increases, the kinetic energy of liquid molecules increases. This weakens intermolecular forces, making it easier for the liquid to flow. As a result, the viscosity of a liquid decreases with an increase in temperature. Effect of Temperature on Gases: - In gases, viscosity is primarily due to the momentum transfer between molecules. As temperature increases, the molecular collisions increase, leading to higher viscosity. Analysis of Options: - Option A: Increase in viscosity of gas → Correct for gases, but the question focuses on general fluid behavior. Option B: Increase in viscosity of liquid → Incorrect, as liquid viscosity decreases with temperature. Option C: Decrease in viscosity of gas → Incorrect, as gas viscosity increases with temperature. Option D: Decrease in viscosity of liquid → Correct, as liquid viscosity reduces when temperature rises. Conclusion : The correct answer is Option D: decrease in viscosity of liquid because higher temperatures reduce intermolecular forces in liquids, allowing them to flow more easily.

Surface tension is indeed a measure of the energy required to increase the surface area of a liquid by a unit amount, and it is commonly expressed in units of energy per unit area (such as N/m or dyn/cm). Option B (distance) is not correct, and option C (both of the above) is not accurate in this context. So, for the specific field of Hydraulics and Fluid Mechanics, the correct answer is option A.

We know that Surface Tension (σ) = Force / Length Step-by-Step Dimensional Analysis: 1. Dimensional Formula of Force (F): - Force = Mass × Acceleration - Acceleration = Length / Time² = LT -2 - So, Force = M × LT -2 = MLT -2 2. Dimensional Formula of Length (L): - L = L 1 3. Dividing Force by Length: - σ = (MLT -2 ) / L - σ = ML (1-1) T -2 = ML 0 T -2 Thus, the correct dimensional formula for surface tension is ML 0 T -2 , making Option B the correct choice .

Bernoulli's theorem states that in an ideal fluid flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant along any streamline. This principle can be applied to various types of flow measurement devices to determine the flow rate of a fluid. The instruments mentioned in the options are commonly used to measure flow based on Bernoulli's theorem. Venturimeter: A venturimeter is a device used to measure the flow rate of a fluid in a pipe by utilizing the principle of Bernoulli's theorem. It consists of a converging section followed by a throat and then a diverging section. The pressure difference between the converging and diverging sections is used to determine the flow rate. Orifice Plate: An orifice plate is another flow measurement device based on Bernoulli's theorem. It consists of a thin plate with a hole (orifice) in it, placed in the pipeline. The pressure difference across the orifice is used to calculate the flow rate. Pitot Tube: A pitot tube is used to measure fluid velocity based on Bernoulli's theorem. It has a pointed end that faces the fluid flow, and a pressure difference is created between the pointed end and the open end of the tube, which is used to determine the fluid velocity. All of the above instruments (Venturimeter, Orifice Plate, and Pitot Tube) are utilized to measure flow by applying Bernoulli's theorem. They exploit the relationship between fluid pressure, velocity, and elevation to determine the flow rate accurately. Therefore, the correct answer is Option D: all of the above .

The tube for sensing the static pressure is known as static tube which surrounds the pitot tube that measures the stagnation pressure.

Manometers are devices in which columns of a suitable liquid are used to measure the difference in pressure between two points or between a certain point and the atmosphere. The manometer is needed for measuring large gauge pressures.

Understanding the Problem: Imagine a wooden block floating in a swimming pool. The block is partially submerged; only a portion of it is underwater. The question asks us to find the weight of this block. Key Concept: Buoyancy When an object floats, the upward force of the water (called buoyant force) equals the weight of the object. The buoyant force is equal to the weight of the water displaced by the submerged part of the object. Calculations: 1. Find the volume of water displaced: The block is submerged to a depth of 0.5 m. The area of the submerged part is length x width = 2 m x 1 m = 2 m². The volume of water displaced is area x depth = 2 m² x 0.5 m = 1 m³ 2. Calculate the weight of the displaced water: Water weighs 10 kN/m³. Therefore, the weight of 1 m³ of water is 1 m³ x 10 kN/m³ = 10 kN 3. Determine the weight of the block: Since the block is floating, the weight of the block equals the buoyant force (weight of the displaced water). Therefore, the weight of the block is 10 kN Correct Answer: The correct option is B: 10 kN

40 m/sec. is the correct answer to “In a two dimensional incompressible steady flow around an airfoil, the stream lines are 2 cm apart at a great distance from the airfoil, where the velocity is 30 m/sec. The velocity near the airfoil, where the stream lines are 1.5 cm apart, is”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

weight of the fluid displaced by the body is the correct answer to “According to the principle of buoyancy a body totally or partially immersed in a fluid will be lifted up by a force equal to”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

$${\text{p}} = \frac{{2{\text{T}}}}{{\text{r}}}$$ is the correct answer to “The difference of pressure between the inside and outside of a liquid drop is”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

cannot remain at rest under action of any shear force is the correct answer to “Fluid is a substance that”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

wake is the correct answer to “The region between the separation streamline and the boundary surface of the solid body is known as”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

the velocity of successive fluid par-ticles, at any point, is the same at suc-cessive periods of time is the correct answer to “Steady flow occurs when”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

zero at the mid plane and varies linearly with distance from mid plane is the correct answer to “The shear stress distribution for a fluid flowing in between the parallel plates, both at rest, is”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

uniform flow is the correct answer to “Normal depth in open channel flow is the depth of flow corresponding to”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

the center of gravity of the body andthe meta center is the correct answer to “Metacentric height is given as the distance between”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

0.611 is the correct answer to “The theoretical value of coefficient of contraction of a sharp edged orifice is”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

laminar flow is the correct answer to “The discharge of a liquid of kinematic viscosity 4 cm 2 /sec through a 8 cm dia-meter pipe is 3200π cm 2 /sec. The type of flow expected is”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

the boundary layer comes to rest is the correct answer to “Separation of flow occurs when”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

the fluid particles move in plane or parallel planes and the streamline pat-terns are identical in each plane is the correct answer to “Two dimensional flow occurs when”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

size and shape of the cross section in a particular length remain constant is the correct answer to “Uniform flow occurs when”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

the energy is constant along a stream-line but may vary across streamlines is the correct answer to “According to Bernoulli’s equation for steady ideal fluid flow”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

as the square of the radial distance is the correct answer to “When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure intensity varies”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.

4°C is the correct answer to “The density of water is 1000 kg/m 3 at”. This question is standard in competitive examination syllabi for Hydraulics And Fluid Mechanics.