Fluid Mechanics — Chapters 1–4 Question Bank

Comprehensive practice flashcards covering fluid properties, fluid statics, basic flow concepts and equations, and fluid resistance in pipe flows based on Chapters 1–4.

What types of forces can a fluid at rest not be subjected to?

tensile forces and shear forces, but can only resist pressure.

What is the weight, in Newton, of a $4\,\text{kg}$ mass on a planet where $g = 10\,\text{m/s}^2$?

$$40\,\text{N}$$

How may a pressure of $10^6\,\text{Pa}$ be written using metric prefixes?

$$\text{MPa}$$

What dimensional property does the bulk modulus of elasticity ($K = -\frac{dp}{dV/V} = \frac{dp}{d\rho/\rho} = \frac{1}{\beta}$) possess?

It has the dimensions of pressure.

For a $14\,\text{MPa}$ increase in pressure, by about what percentage has the density of water increased (given $K$ of water is $2.1\,\text{GPa}$)?

$$\frac{2}{3}\%$$

If a pressure of $4.1\,\text{MPa}$ applied to $10\,\text{m}^3$ of liquid causes a volume reduction of $0.02\,\text{m}^3$, what is the bulk modulus of elasticity in $\text{Pa}$?

$$2\,050\,000\,000\,\text{Pa}$$

What is the correct SI unit for dynamic viscosity, $\mu$?

$$\text{kg}/(\text{m}\cdot\text{s})$$

What is the correct SI unit for kinematic viscosity, $\nu$?

$$\text{m}^2/\text{s}$$

For $\mu = 0.07\,\text{kg}/(\text{m}\cdot\text{s})$ and relative density $\text{RD} = 0.70$, what is the kinematic viscosity $\nu$ in stokes ($1\,\text{cm}^2/\text{s} = 1\,\text{St}$)?

$$1.0\,\text{St}$$

A liquid has a kinematic viscosity of $3 \times 10^{-4}\,\text{m}^2/\text{s}$ and a density of $700\,\text{kg/m}^3$. What is its dynamic viscosity in SI units?

$$0.21\,\text{kg}/(\text{m}\cdot\text{s})$$

What equation does a perfect gas satisfy?

It satisfies Equation (1.21): $p u = R T$

What are the two defining characteristics of an ideal fluid?

It has zero viscosity and is incompressible.

Under what condition is the pressure at a point in a fluid identical in all directions?

Only when the fluid is at rest.

What is the base level of measurement used for relative (gauge) pressure?

Local atmospheric pressure.

What is the absolute pressure at a depth of $10\,\text{m}$ in a water reservoir?

$$199.38\,\text{kPa (abs)}$$

How may an absolute pressure of $400\,\text{mmHg abs}$ be expressed when the barometer reading is $720\,\text{mmHg}$?

$$320\,\text{mmHg vacuum}$$

When the barometer reads $100\,\text{kPa}$, what is a suction of $10\,\text{kPa}$ equivalent to in relative pressure?

$$-10\,\text{kPa}$$

What is true regarding the position of the center of pressure on a submerged plane area?

The pressure center is always below the centroid of the submerged area.

How do fluid particles move in laminar flow?

A layer of fluid particles moves relatively smooth upon another layer of particles, the particles are not mixed with each other, and there is no lateral movement.

What is the defining characteristic of uniform flow?

At every point over the cross section the velocity vector is identically the same along the flow direction, and the streamline is parallel line.

For a one-dimensional flow along coordinate $s$, how is the total acceleration expressed?

$$u \frac{\partial u}{\partial s} + \frac{\partial u}{\partial t}$$

In a one-dimensional steady flow with velocity $u$, how is the acceleration $a$ expressed?

$$u \frac{\partial u}{\partial s}$$

Given the velocity field $u_x = -ky$, $u_y = kx$, and $u_z = 0$, what is the streamline equation?

$$x^2 + y^2 = C$$

In fluid mechanics flow analysis, what is a cross section defined as?

A plane.

What is the unit of volumetric flow rate?

$$\text{m}^3/\text{s}$$

What is true about the mass of a closed thermodynamic system?

The mass of a system is definite.

What is true about the mass in a control volume?

It is mass that can pass through the control surface.

In the continuity equation $\rho_1 V_1 A_1 = \rho_2 V_2 A_2$, how must the fluid density be evaluated?

As the average value over the section.

Under what flow conditions does the equation $\frac{\partial u_x}{\partial x} + \frac{\partial u_y}{\partial y} + \frac{\partial u_z}{\partial z} = 0$ apply?

Incompressible fluid, steady flow and unsteady flow.

What conditions are required to apply Bernoulli’s equation along a streamline for an ideal fluid?

Steady flow, incompressible fluid, gravity field.

What three heads constitute the total head in Bernoulli’s equation?

Elevation head, pressure head, velocity head.

When a fluid system does work on its surroundings, under what condition is the process reversible?

If the fluid is an ideal fluid that the viscosity is neglected.

For a liquid system undergoing an irreversible process, what effect do mechanical energy losses have?

They cause the temperature to increase.

For steady, incompressible flow with no heat exchange across a hydroelectric dam, which downstream parameter changes due to power generation and mechanical losses?

The temperature of water.

How is gradually varied flow characterized geometrically?

The angle of arbitrary two streamlines is very small and the curvature of each streamline is very small.

At what types of sections should cross sections for total flow analysis be selected?

At the section in gradually varied flow or the section in uniform flow.

What does the Reynolds upper critical number represent?

A critical value while laminar flow turns into turbulent flow.

What is the formula for the Reynolds number in a circular pipe?

$$\frac{V D}{\nu}$$

What is the Reynolds lower critical number for circular pipe flow?

$2000$ (or $2320$)

What does the hydraulic diameter represent for a pipeline?

The characteristic dimension of pipeline.

What is the kinetic energy correction factor $\alpha$ for laminar flow in a circular tube?

$$\alpha = 2$$

What is the momentum correction factor $\beta$ for laminar flow in a circular tube?

$$\beta = \frac{4}{3}$$

How is shear stress distributed over the cross section of a round tube in laminar flow?

The shear stress at the axis of pipe is zero and has linear relation to the radius.

How is the discharge of laminar flow in a circular pipe related to fluid viscosity?

It is inversely proportional to fluid viscosity.

When a circular pipe is inclined, what expression replaces $\frac{dp}{dx}$ in the equation $u_{\max} = -\frac{a^2}{4\mu}\left(\frac{dp}{dx}\right)$?

$$-\frac{d(p + \rho g h)}{dx}$$

What is a correct statement regarding the boundary layer thickness?

The thickness of boundary-layer is relevant to the Reynolds number.

Which set of variables is suitable to determine the friction coefficient of turbulent flow in a smooth pipe?

$V$, $D$, $\mu$, $\rho$

Which single factor from $\text{Re only}$, $\text{Re}$, $\lambda, V$, or $Q\text{ only}$ is sufficient by itself to determine loss in a rough pipe?

None of the above (determination requires both relative roughness and Reynolds number).

What are the head losses at the exit of a pipe located at the bottom of a tank?

$$0.5\frac{V^2}{2g}$$