Applied Hydraulics

Density is defined as?

Mass per unit volume

The formula for discharge (Q) in a pipe with cross-sectional area (A) and velocity (v) is:

Q=A×v

what defines a "fluid" in the context of hydraulics?

A substance that deforms continuously under the application of shear stress.

What is the standard SI unit for pressure? 

Pascal (Pa)

In the English system, discharge is often measured in "cfs." What does this stand for?

Cubic feet per second

“Discharge" in hydraulics refers to:

The volume of fluid passing through a cross-section per unit of time.

Pressure is mathematically defined as:

Force divided by Area

At 4◦C, water has its:

Maximum density

Pressure exerted by a fluid at rest is always ____________ to the surface.

Perpendicular

Which instrument is used to measure atmospheric pressure?

Barometer

A manometer fluid should have a density that is:

Significantly higher than the fluid being measured

”Atmospheric Pressure” is caused by:

Weight of the air above

Absolute pressure is equal to:

Gage pressure + Atmospheric pressure

According to Pascal’s Law, pressure applied to an enclosed fluid is:

Transmitted undiminished in all directions

Ideal fluids are assumed to have __________ viscosity.

Zero

A piezometer is a simple device used to measure:

Moderate liquid pressures in a pipe

The SI unit for Mass is:

Kilogram

Dimensional homogeneity is a requirement for:

All valid physical equations

in the formula P = ρgh, h represents:

Vertical depth below the free surface

Which property of a fluid is defined as its mass per unit volume?

Density

Which of the following is NOT a property of a fluid?

Ductility

An object weighs 50 N in air and 30 N when fully submerged in an unknown liquid. What is the buoyant force exerted by the liquid?

20 N

If an object is floating in a container of water, what can you conclude about the buoyant force acting on it?

The buoyant force is equal to the weight of the object.

A rectangular barge is 10 m long and 4 m wide. When placed in water the barge sinks 0.05 m into the water. What is the "mass" of the crate?

Use: Density of water: 1000 kg/m3. Acceleration due to gravity (g): 9.8 m/s2

2,000 kg

A solid cube with a side length of 0.1 m is completely submerged in water.  Density of water: 1000 kg/m3. Acceleration due to gravity (g): 9.8 m/s2

What is the magnitude of the buoyant force acting on the cube?

9.8 N

If an object is completely submerged and then pushed deeper into a pool of water (assume the density of water is constant), what happens to the buoyant force acting on it?

It remains the same.

A solid sphere is floating in a liquid with half of its volume submerged. If the entire system is taken to the Moon, where gravity is one-sixth that of Earth, what fraction of the sphere will be submerged?

Half of the volume.

A metal sphere with a radius of 0.05 m is dropped into a pool of mercury (density =13,600 kg/m3). What is the approximate buoyant force on the sphere if it is fully submerged?

Density of water: 1000 kg/m3. Acceleration due to gravity (g): 9.8 m/s2

69.7 N

A block of wood and a block of iron are the exact same size (and same volume). If both are held completely submerged under water, which one experiences a larger upward buoyant force?

Both experience the same buoyant force.

A wooden block has a volume of 0.02 m3 and a density of 600 kg/m3. If it is placed in water, what volume of the block will be submerged below the surface?

Use: Density of water: 1000 kg/m3. Acceleration due to gravity (g): 9.8 m/s2

0.012 m3 

A container of water is placed on a sensitive weighing scale. A finger is dipped into the water without touching the bottom or sides of the container. What happens to the reading on the scale?

The reading increases by the weight of the water displaced by the submerged part of the finger. D) The reading decreases because the finger exerts an upward force on the water.

A person floats in a swimming pool; if the same person transitions from a freshwater pool to the Great Salt Lake (with high salt content), they float significantly higher. Why does this occur?

Saltwater is denser than freshwater, requiring less displaced volume to equal the person's weight.

What is the primary reason that a solid piece of iron sinks in water, but a huge ship made of iron floats?

The ship contains a large volume of air, making its average density less than water.

Which of the following represents the correct dimensions for "Pressure" in the M L T system?

ML⁻¹T⁻²

The principle of "Dimensional Homogeneity" states that:

Every term in a physical equation must have the same dimensions.

What are the dimensions for "Dynamic Viscosity" (μ) in the M L T system? (Hint: Viscosity = Shear Stress / Velocity Gradient)

ML⁻¹T⁻¹

According to Pascal's Paradox, three containers of different shapes (slanted, vertical, and stepped) with the same base area and filled to the same height (h) with the same liquid will have:

Equal pressure at the base but different total weights of liquid.

Which of the following is the correct dimension for "Force" (F)?

MLT⁻²

In the equation P=ρgh, the term ρg represents "Specific Weight." What are its dimensions?

ML⁻²T⁻²

Why is it called "Pascal's Paradox"?

Because the total force on the base can be greater or less than the actual weight of the liquid in the vessel.

Which of the following is a "Dimensionless" quantity?

Kinematic Viscosity

Specific Gravity

Mass Density

 Pressure Head

Specific Gravity

What are the M L T dimensions for "Work" or "Energy"?

ML²T⁻²

If an equation is "Dimensionally Homogeneous," does it mean the equation is definitely physically correct?

No, an equation can be homogeneous but still be missing a dimensionless constant or have the wrong physical relationship.

Over time, the inner walls of an older cast iron pipe become scaled and corroded. How does this aging affect the system's hydraulics?

The absolute roughness (ϵ) increases, the friction factor (f) increases, and head losses increase.

A sudden contraction in a pipe causes a minor head loss. The primary reason for this loss is:

The increase in wall friction due to the higher velocity in the smaller pipe.

if the diameter of a pipe is reduced by half while maintaining the same volumetric flow rate, how does the head loss due to friction change? (Assume the friction factor f remains approximately constant for estimation). Head loss (HL) is = fLV²/(2gD)

It increases by a factor of 32.

In the context of Bernoulli’s equation, "Head" is a way of expressing energy in terms of:

Length (Elevation)

Water flows through a converging pipe flowing upwards. The velocity increases from station 1 to station 2. What can be concluded about the static pressure P2​ compared to P1​?

A. P2​ is definitely greater than P1​.

B. P2​ is definitely less than P1​.

C. P2​ is exactly equal to P1​.

D. The relationship between P2​ and P1​ cannot be determined without knowing the exact elevation change and velocities.

B. P2​ is definitely less than P1​.

A pipeline connects two reservoirs with a difference in surface elevation of Δz.

If the flow is steady, the total head loss in the pipeline (friction + minor losses) is equal to:

The elevation difference, Δz.

In the context of pipe networks, the head loss in two pipes connected in parallel must be:

Equal to each other.

When fluid flows through a sudden expansion in a pipe, the major source of mechanical energy loss is due to:

The formation of eddies and flow separation in the corners of the expansion.

A piezometer tube is connected to the side of a pipe where water is flowing. The height of the water column in the piezometer measures the:

Static pressure head.

A system curve starts at a non-zero Head (H) value when Flow (Q) is zero. This value represents:

A. The friction loss.

B. The static head (elevation difference).

C. The vapor pressure.

D. The pump's shut-off head.

B. The static head (elevation difference).

If two identical pumps are placed in series, the result is:

A. Twice the flow at the same head.

B. Twice the head at the same flow.

C. Higher efficiency than a single pump.

D. Reduced risk of cavitation.

Twice the head at the same flow.

How does increasing the fluid temperature affect the NPSHa of a system?

A. NPSHa increases because the fluid becomes less dense.

B. NPSHa decreases because the vapor pressure of the liquid increases.

C. NPSHa remains constant because it only depends on the pump speed.

D. NPSHa increases because the viscosity decreases, reducing friction losses.

NPSHa decreases because the vapor pressure of the liquid increases.

In a parallel pump configuration (two identical pumps), the combined characteristic curve is found by:

A. Doubling the head for every flow rate.

B. Doubling the flow rate for every head value.

C. Adding the efficiencies together.

D. Doubling the power requirement while keeping flow constant.

B. Doubling the flow rate for every head value.

Friction head loss (Hf​) in the suction pipe is calculated using:

A. The pump curve.

B. The Darcy-Weisbach or Hazen-Williams equation.

C. The vapor pressure table.

D. The pump’s specific speed.

B. The Darcy-Weisbach or Hazen-Williams equation.

Cavitation damage is usually found on:

A. The motor windings.

B. The discharge piping only.

C. The impeller vanes (usually near the eye or inlet).

D. The external casing bolts.

C. The impeller vanes (usually near the eye or inlet).

Real-life Application: A pump is cavitating. You decide to lower the pump by 3 feet. Which Bernoulli variable are you changing to fix the problem?

A. You are decreasing hL​ by shortening the pipe.

B. You are increasing the static head component (z1​−z2​) of the suction side.

C. You are increasing the atmospheric pressure.

D. You are decreasing the vapor pressure of the fluid.

You are increasing the static head component (z1​−z2​) of the suction side.

A real-life cooling water system uses a strainer on the suction pipe. If the strainer becomes 50% clogged, how does this affect the Bernoulli energy balance for the pump?

A. hL​ (head loss) increases, thereby decreasing the pressure P2​ at the pump inlet.

B. z2​ increases, making the pump physically higher.

C. The vapor pressure Hvp​ of the water decreases.

D. The atmospheric pressure P1​ increases to compensate.  

 

hL​ (head loss) increases, thereby decreasing the pressure P2​ at the pump inlet.

For a "Submerged" pump (where the source water surface is higher than the pump), the elevation head z in the Bernoulli equation acts as:

A. A penalty that reduces the pressure at the inlet.

B. A "Static Suction Head" that increases the pressure at the inlet, improving NPSHa.

C. A friction factor.

D. A variable that only affects the pump's efficiency, not NPSH.

A "Static Suction Head" that increases the pressure at the inlet, improving NPSHa.

A "flat" pump curve or pump characteristic curve is one where:

A. The head changes significantly with a small change in flow.

B. The head remains relatively constant over a wide range of flow.

C. The efficiency is always 100%.

D. The pump cannot handle high pressures.

The head remains relatively constant over a wide range of flow.

When a fluid enters the impeller eye, it undergoes local acceleration. According to Bernoulli, this acceleration causes a localized pressure "dip (i.e., gets lowered)." Cavitation occurs if this dip reaches:

A. The atmospheric pressure (Patm​).

B. The vapor pressure (Pvp​) of the liquid at the operating temperature.

C. Zero gauge pressure.

D. The shut-off head of the pump.

To prevent cavitation, a common engineering rule of thumb is to ensure:

A. NPSHa=NPSHr.

B. NPSHa≥NPSHr+margin (usually 0.5 to 1.0 m).

C. NPSHa<NPSHr.

D. NPSHr is as high as possible.

NPSHa≥NPSHr+margin (usually 0.5 to 1.0 m).

Cavitation in a centrifugal pump most likely occurs when:

A. NPSHa > NPSHr

B. The pump is running at a very low speed.

C. The local pressure drops below the vapor pressure of the liquid.

D. The discharge valve is completely closed.

C. The local pressure drops below the vapor pressure of the liquid.

Which of the following will decrease the NPSHa of a pumping system?

A. Increasing the diameter of the suction pipe.

B. Lowering the pump closer to the water source.

C. Increasing the friction losses in the suction line (e.g., a clogged strainer).

D. Increasing the atmospheric pressure.

C. Increasing the friction losses in the suction line (e.g., a clogged strainer).

If you increase the suction pipe diameter from 4 inches to 6 inches, how does the Bernoulli "friction Loss" term (hL​) change for a constant flow rate?

A. It increases because there is more surface area for friction.

B. It decreases because the velocity (v) decreases, and hL​ is proportional to v2.

C. It stays the same because the flow rate (gpm) is unchanged.

D. It increases because the fluid is moving more slowly.

B. It decreases because the velocity (v) decreases, and hL​ is proportional to v2.

Which component of the System Curve increases with the square of the flow rate (Q²)?

A. Static Head.

B. Friction Head.

C. NPSHr.

D. Vapor Pressure.

B. Friction Head.

If a suction pipe is undersized (too small in diameter), the Bernoulli equation shows that the velocity head (v²/2g) will be very high. How does this specifically impact the pump?

A. It increases the NPSHa because the fluid is moving faster.

B. It decreases NPSHa because higher velocity results in higher friction losses and lower static pressure.

C. It reduces the NPSHr of the pump.

D. It has no impact on cavitation risk.

B. It decreases NPSHa because higher velocity results in higher friction losses and lower static pressure.

NPSHr (Required) is determined by:

A. The elevation of the reservoir.

B. The pipe diameter and length.

C. The pump manufacturer through testing.

D. The temperature of the fluid being pumped.

C. The pump manufacturer through testing.

The operating point (duty point) of a pumping system is found at:

A. The intersection of the Pump Curve and the System Curve.

B. The maximum point of the Efficiency Curve.

C. The point where NPSHa is exactly zero.

D. The shut-off head.

A. The intersection of the Pump Curve and the System Curve.

You are selecting a pipe material for a long suction line. Why is a smooth interior (lower C factor in Hazen-Williams) preferred for NPSH considerations?

A. It increases the vapor pressure of the water.

B. It reduces the hf​ (friction loss) term in the Bernoulli equation, maximizing pressure at suction inlet​ of a pump. 

C. It allows the pump to spin faster.

D. It increases the static head of the reservoir.

B. It reduces the hf​ (friction loss) term in the Bernoulli equation, maximizing pressure at suction inlet​ of a pump. 

Which of the following defines non-conservative Net Positive Suction Head Available (NPSHa)?

A. The pressure required by the pump manufacturer to prevent cavitation.

B. The total suction head minus the vapor pressure of the liquid at the suction nozzle.

C. The difference between the discharge pressure and the suction pressure.

D. The head loss due to friction in the discharge piping.

B. The total suction head minus the vapor pressure of the liquid at the suction nozzle.

If you need to increase the flow rate in a system with high friction losses, you should:

A. Install a smaller pump.

B. Add a second pump in series.

C. Add a second pump in parallel.

D. Close the suction valve slightly.

C. Add a second pump in parallel.

Why is the "Velocity Head" (v²/2g) term at the pump suction nozzle excluded in the non-conservative NPSHa calculation? 

A. Because it represents kinetic energy that can be converted back into pressure.

B. Because it increases the vapor pressure of the liquid.

C. Because it represents a friction loss.

D. It is actually subtracted because high velocity causes a pressure drop.

A. Because it represents kinetic energy that can be converted back into pressure.

What happens to the system curve if a valve on the suction side is partially closed?

A. It shifts to the left (becomes steeper).

B. It shifts to the right (becomes flatter).

C. It shifts downward.

D. It remains unchanged.

A. It shifts to the left (becomes steeper).

What is the primary purpose of the volute in a centrifugal pump casing?

A. To increase the velocity of the fluid as it exits the impeller.

B. To convert kinetic energy into pressure energy by gradually increasing the flow area.

C. To balance the axial thrust on the pump shaft.

D. To cool the mechanical seals during high-speed operat

B. To convert kinetic energy into pressure energy by gradually increasing the flow area.

Specific Energy in an open channel is defined as the total energy head measured relative to:
A. A standardized sea-level datum.
B. The water surface.
C. The channel bottom.
D. The energy grade line.

C. The channel bottom.

If the Froude number is less than 1.0, the flow is classified as:
A. Supercritical
B. Subcritical
C. Critical
D. Transitional

B. Subcritical

In Manning's equation, the hydraulic radius is defined as the:
A. Cross-sectional area divided by the wetted perimeter.
B. Wetted perimeter divided by the cross-sectional area.
C. Top width of the channel divided by the depth.
D. Cross-sectional area divided by the top width.

A. Cross-sectional area divided by the wetted perimeter.

A sharp-crested weir is a hydraulic structure primarily designed to:
A. Dissipate excess kinetic energy.
B. Induce a hydraulic jump.
C. Measure or control discharge.
D. Prevent downstream scouring.

C. Measure or control discharge.

Uniform flow in an open channel occurs when:
A. The flow rate changes gradually over time.
B. The water surface is perfectly flat and horizontal.
C. Flow parameters (depth, velocity, cross-section) remain constant with respect to distance along the channel.
D. The Froude number is exactly equal to 1.0.

C. Flow parameters (depth, velocity, cross-section) remain constant with respect to distance along the channel.

Which of the following best defines steady flow in an open channel?
A. The depth of flow remains constant along the length of the channel.
B. The velocity of flow remains constant along the length of the channel.
C. Flow parameters (depth, velocity, discharge) do not change with respect to time at a given location.
D. Flow parameters change at a constant rate with respect to time.

C. Flow parameters (depth, velocity, discharge) do not change with respect to time at a given location.

Normal depth is the depth of flow that occurs under which conditions?
A. When the flow is critical.
B. When the flow is uniform and steady.
C. When specific energy is at a minimum.
D. When the channel slope is zero.

B. When the flow is uniform and steady.

Manning's equation is primarily utilized to calculate variables associated with:
A. Unsteady, rapidly varied flow.
B. Uniform flow.
C. Hydraulic jumps.
D. Flow over a sharp-crested weir.

B. Uniform flow.

The most hydraulically efficient channel cross-section is the one that has:
A. The maximum wetted perimeter for a given area.
B. The minimum wetted perimeter for a given area.
C. The maximum roughness coefficient.
D. The steepest bed slope.

B. The minimum wetted perimeter for a given area.

An unsteady, non-uniform flow is best represented by which of the following scenarios?
A. Water flowing at a constant rate through a long, straight prismatic concrete channel.
B. A flood wave traveling down a natural river.
C. Flow over a spillway at a constant discharge.
D. Flow behind a dam before the gates are opened.

B. A flood wave traveling down a natural river.

At critical depth, the specific energy for a given discharge is:
A. At a maximum.
B. Zero.
C. Equal to the flow depth.
D. At a minimum.

D. At a minimum.

According to Pascal's Paradox, three containers of different shapes (slanted, vertical, and stepped) with the same base area and filled to the same height (h) with the same liquid will have:

Equal pressure at the base but different total weights of liquid.

If a force of 500 N is applied to a piston with an area of 0.05 m², what is the pressure generated in the fluid?

10,000 Pa

When identifying a "line of equal pressure" in a static fluid for manometer calculations, which condition MUST be met?

The points must be at the same horizontal level and within the same continuous fluid.

A hydraulic press has two pistons with diameters in a ratio of 1:5. If a force of 100 N is applied to the smaller piston, what is the approximate theoretical force exerted by the larger piston?

2500 N

What is the "Weight" of 2 m³ of a fluid that has a mass density of 1000 kg/m³? (Assume g=9.81 m/s²)

19620 N

In soil mechanics and civil engineering, how does the "capillary effect" impact the foundation of a structure?

A) It creates a vacuum that pulls the foundation downward.

B) It allows groundwater to rise above the water table through narrow soil pores, potentially damaging the structure.

C) It increases the atmospheric pressure acting on the soil.

D) It reduces the surface tension of the groundwater, making it more acidic.

B) It allows groundwater to rise above the water table through narrow soil pores, potentially damaging the structure.

Which of the following represents the correct dimensions for "Pressure" in the M L T system?

ML⁻¹T⁻²

The pressure measured by a standard gauge is 40 kPa. If the local atmospheric pressure is 101 kPa, what is the "Absolute Pressure"?

141 kPa

An "Inclined Manometer" is specifically designed to:

Increase the sensitivity of the reading by magnifying the liquid's travel distance.

f a barometer were filled with water instead of mercury (with Specific Gravity 13.6), how tall would the glass tube need to be to measure standard atmospheric pressure? Mercury-based barometer registers 760 mm in the tube.

10.3 meters

If a closed tank is half-full of oil and the air space above it is pressurized to 20 kPa (gauge), what is the pressure at a point 2 meters below the oil surface? (ρ_oil​=800 kg/m³). Take g=9.81 m/s²

35.69 kPa