Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on quizzes and to give dedicated students a chance to learn the course material more thoroughly. Most of the questions in the testbank can be done in a short amount of time, although there are some numerical questions that require more thought. A few of the multiple-choice questions were taken directly from previous quizzes, and I plan to use some of these questions in future quizzes and tests to reward students who use the testbank. Questions included with this sample testbank are mostly from the areas of fluids properties and hydrostatics, although there are also a few questions related to fluid dynamics. In the future I plan to expand the testbank to include questions from all of the subject areas that are currently taught in the class.
Questions Section 1: Fluids Properties 1. According to Newton's law of viscosity, the shear stress in a fluid is. (a) inversely proportional to the depth of the fluid (b) proportional to the depth of the fluid (c) inversely proportional to the velocity gradient in the fluid (d) proportional to the velocity gradient in the fluid Correct Answer: (d) 2. What is the primary difference between dynamic viscosity (µ) and kinematic viscosity (ν)? (a) Kinematic viscosity is independent of pressure. (b) Dynamic viscosity is independent of pressure. (c) Dynamic viscosity is independent of temperature. (d) Kinematic viscosity is independent of temperature. Correct Answer: (b) Type: Fill in the blank Randomization: None Notes: (i) It would be easy to change this problem so that the distance between the plates, the relative velocity of the plates or the viscosity of the fluid changes each time the student redoes the problem. (ii) The units required in numerical problems are somewhat cumbersome for students. I have not yet found a way to do a fill-in the blank problem that specifies the units for the student. 3. The relative velocity of two infinitely wide parallel plates that are 1 cm apart is 10 cm/s. If the dynamic viscosity of the liquid between the plates is 0.001 N s/m 2, what is the shear stress between the plates? Correct Answer: use Newton s law of viscosity
Type: Fill in the blank Randomization: None Notes: This problem could easily be changed so that the distance from the wall or the viscosity of the fluid changes each time the student redoes the problem. 4. If the dynamic viscosity of the fluid shown in the diagram is 0.001 N s/m 2, what is the shear stress 0.25 m from the wall? Hin t 1: Differentiate first... then plug in a value for y. Correct Answer: differentiate the equation and use Newton s law of viscosity Type: Fill in the blank Randomization: Weight of block is varied between 1 and 8 Newtons 5. A block that weighs {1:8} N slides down an incline on a thin viscous fluid layer. The bottom of the block has a surface area of 1 m 2. If the dynamic viscosity of the fluid is 0.001 N s/m2, what is the terminal velocity of the block? Hint 1: Draw a force diagram and consider only the force components in the direction of motion of the block. Use Newton's law of viscosity to represent the friction force opposing the block's motion. Correct Answer: use Newton s law of viscosity to determine shear stress and apply the shear stress to the bottom of the block
Type: Fill in the blank Randomization: Specific weight of fluid is varied between 500 and 13000 N/m 3 Volume of fluid is varied between 0.5 and 10.5 m 3 6. If the specific weight of a fluid is {500:13000} N/m 3, what is the weight of {0.5:10.5} m 3 of the fluid? Correct Answer: The weight is the product of the specific weight and the volume Type: Fill in the blank Randomization: Density of fluid is varied between 100 and 1300 kg/m 3 7. If the density of a fluid is {100:1300} kg/m 3, what is the specific weight of the fluid? Correct Answer: The specific weight is the product of the density and gravitational acceleration 8. Which is true of a liquid? (a) Its viscosity increases with temperature. (b) The primary cause of its viscosity is momentum transfer by random molecular motion. (c) Its density is much lower than that of a gas. (d) The primary cause of its viscosity is cohesion between adjacent molecules. Correct Answer: (d) Type: Fill in the blank Randomization: Specific gravity is varied between 0.8 and 2. 9. If the specific gravity of a fluid is {0.8:2}, what is the density of the fluid? Correct Answer: Density is the product of the specific gravity and the density of water at 20 C (1000 kg/m 3 )
10. The constant of proportionality in Newton's law of viscosity is. (a) The velocity gradient of the fluid. (b) The dynamic viscosity of the fluid. (c) The kinematic viscosity of the fluid. (d) The velocity of the fluid. Correct Answer: (b) Randomization: None (c) and (d) require constant positions 11. The speed of sound in water is a function of. (a) The density of the water (ρ) (b) The bulk modulus of the water (E) (c) Neither (a) nor (b) (d) Both (a) and (b) Correct Answer: (d) Type: Fill in the blank Randomization: Speed of sound in the fluid is varied between 1000 and 2000 m/s and the bulk modulus the fluid is varied between 1000000000 and 2000000000 N/m 2 12. If the bulk modulus of a fluid is {1000000000:2000000000} N/m 2 and the speed of sound in the fluid is {1000:2000} m/s, what is the density of the fluid? Correct Answer: Density equals the bulk modulus divided by the square of the speed of sound.
Section 2: Hydrostatics 1. What is the primary advantage of using a tainter gate instead of a vertical sluice gate? (a) A Tainter gate does not leak as readily as a sluice gate (b) A Tainter gate is less costly to construct than a sluice gate (c) The pressure forces on a tainter gate do not create a moment about the gate's rotation axis (d) A Tainter gate can withstand much higher pressures than a sluice gate (e) A Tainter gate weighs less than a sluice gate Correct Answer: (c) 2. The magnitude of the buoyancy force on a submarine submerged in a lake equals: (a) The weight of the lake water displaced by the submarine (b) The weight of the submarine (c) The product of the volume of the submarine and the density of the water surrounding the submarine (d) The density of the water displaced by the submarine Correct Answer: (a) 3. How does the pressure in a hydrostatic fluid vary? (a) The pressure decreases exponentially with depth (b) The pressure increases exponentially with depth (c) The pressure increases linearly with depth (d) The pressure decreases linearly with depth Correct Answer: (c)
Type: Selectable Image Randomization: None Notes: Student can use the mouse to select the image that best fits the description 4. Select the image that depicts the most likely distribution of pressure on a sphere submerged in a liquid. Correct Answer: upper left corner Randomization: Order of solutions. Depth varies from 4 to 15 m. Density varies from 800 to 1500 kg/m 3. Notes: Both right and wrong answers depend on input variables. 5. What is the gage pressure at a depth of {4:15} m in a liquid with a density of {800:1500} kg/m 3? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Pressure equals the product of the depth, the density, and the gravitational acceleration.
Randomization: Order of solutions. Height of mercury varies from 730 to 790 mm. Notes: Both right and wrong answers depend on input variables. 6. If the mercury in the tube has a density of 13550 kg/m 3 and rises to a height, h m, of {730:790} mm, what is the atmospheric pressure? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Pressure equals the product of h m and the specific weight of mercury. Randomization: Order of solutions. h m varies from 5 to 10 cm. h o is always h m /2. Notes: Both right and wrong answers depend on input variables. 7. The figure shows the cross section of an oil pipe with a manometer attached. On the right side of the manometer the manometer fluid is in contact with oil, and on the left side the manometer is open to the atmosphere. The oil has a specific gravity of 0.85 and the manometer fluid has a specific gravity of 1.5. What is the gage pressure at the center of the pipe if hm is {5:10} cm and ho is {2.5:5} cm? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Pressure equals γ water (s m h m -s o h o ) where γ water is the specific weight of water and s m and s o are the specific gravities of the manometer fluid and the oil, respectively.
Randomization: Order of solutions. h m varies from 10 to 20 cm and s m varies from 0.8 to 1.6. Notes: Both right and wrong answers depend on input variables. 8. The figure shows the cross section of a water pipe with a manometer attached. On the left side of the manometer the manometer fluid is in contact with the water, and on the right side the manometer is open to the atmosphere. The manometer fluid has a specific gravity of {0.8:1.6}. What is the gage pressure at the center of the pipe if h m is {10:20} cm and h w is 10 cm? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Pressure equals γ water (-s m h m -h w ) where γ water is the specific weight of water and s m is the specific gravity of the manometer fluid. Randomization: Order of solutions. Volume varies from 0.0001 to 0.0008 m 3. Specific gravity of the fluid varies from 0.7 to 1.7. Notes: Both right and wrong answers depend on input variables. 9. A bottle has a volume of {0.0001: 0.0008} m 3 and a weight of 1 N. If the bottle is submerged in a fluid with a specific gravity of {0.7:1.7}, the buoyancy force on the bottle will be: (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Buoyancy equals the product of the bottle volume and the specific weight of the fluid that surrounds it.
Randomization: Order of solutions. Depth varies from 3 to 10 m. Width varies from 4 to 10 m. Notes: Both right and wrong answers depend on input variables. 10. Water (γ = 9810 N/m 3 ) is held back by a tainter gate as shown in the profile, below. The vertical distance from the water surface to the spillway crest, h c, is {3:10} meters. If the gate is {4:10} meters wide (into the page), what is the horizontal force on the gate? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: Horizontal force equals the product of the specific weight, the width and height of the gate, and the location of the centroid of the gate below the water surface. Problem is simplified because we can just look at the projection of the gate onto a vertical plane. Randomization: Order of solutions. Depth varies from 3 to 10 m. Width varies from 4 to 10 m. Notes: Both right and wrong answers depend on input variables. 11. Water (γ = 9810 N/m 3 ) is held back by a tainter gate as shown in the profile, below. The vertical distance from the water surface to the spillway crest, h c, is {3:10} meters. If the gate is {4:10} meters wide (into the page), what is the location of the horizontal resultant force on the gate? (a) {Answer depends on input variables} (b) {Answer depends on input variables} (c) {Answer depends on input variables} (d) {Answer depends on input variables} Correct Answer: The center of pressure (not the centroid) of a projection of the gate onto a vertical plane must be found.
Type: Selectable Image Randomization: None Notes: Student can use the mouse to select the image that best fits the description 12. A rectangular container has a semi-cylindrical volume attached to the base as shown on the left. The container is filled with fluid. What volume must be used to compute the vertical force on the quarter-cylindrical curved surface identified as A- B (select one of the shaded areas on the right)? Comment: To calculate the vertical force on a curved surface, you must compute the volume of fluid that WOULD be directly above the surface if the surface was completely surrounded by fluid. The weight of fluid necessary to fill the volume above the surface is the magnitude of the force. Correct Answer: upper right corner. The vertical force is the product of the specific weight of the fluid and the volume above the curved surface and below the fluid free surface
Section 3: Fluid Dynamics 1. A fluid that can be considered to be both incompressible and frictionless is called: (a) A laminar fluid (b) A turbulent fluid (c) A viscous fluid (d) An Eulerian fluid (e) An ideal fluid Correct Answer: (e), fluid may be a gas or a liquid, temperature may increase or decrease. 2. Assume that the diameter of a pipe and the velocity of the flow in the pipe are fixed. If the temperature of a {gas, liquid} flowing through the pipe {increases, decreases}, the Reynolds number of the flow most likely: (a) increases (b) decreases (c) stays the same Correct Answer: depends on question form. Reynolds number is inversely related to viscosity, and viscosity is a function of temperature (however, the function is different for gases and liquids).
Section 4: Closed Conduit Flow Randomization: None (because fixed order is necessary for (e)) 1. Which of the following can be used to calculate friction factors for turbulent flows? (a) The Colebrook-White Equation (b) The Swamee-Jain forumla (c) The Moody Diagram (d) Blasius' Equation (e) All of the above Correct Answer: (e) Randomization: None (because fixed order is necessary for (e)) 2. What is the velocity correction factor, α, for laminar closed conduit flow? (a) 2.0 (b) 1.1 (c) 1.05 (d) 1.0 (e) None of the above Correct Answer: (a) Randomization: None (because fixed order is necessary for (e)) 3. What is the empirical value of the velocity correction factor, α, for fully turbulent closed conduit flow? (a) 2.0 (b) 1.1 (c) 1.05 (d) 1.0 (e) None of the above Correct Answer: (c)
Randomization: Order of options 4. For closed conduit flow in a circular pipe, what is the Reynolds number below which the flow is exclusively laminar? (a) 500 (b) 2000 (c) 1000 (d) 10000 (e) 3000 Correct Answer: (b) Randomization: None (because fixed order is necessary for (e)) 5. Which of the following can be used to calculate friction factors for laminar flows? (a) The Colebrook-White Equation (b) 64/Re (c) The Swamee-Jain Equation (d) Blasius equation (e) All of the above Correct Answer: (b)
Section 5: Boundary Layer Flow Randomization: Order of options 1. For open channel flow, what is the Reynolds number below which the flow is exclusively laminar? (a) 500 (b) 2000 (c) 1000 (d) 10000 (e) 3000 Correct Answer: (a) Randomization: Order of options 2. For flow between two plates of infinite extent, what is the Reynolds number below which the flow is exclusively laminar? (a) 500 (b) 2000 (c) 1000 (d) 10000 (e) 3000 Correct Answer: (c) Randomization: Order of options, Question may ask for either closed conduit or open channel flow. 3. For {open channel flow : closed conduit flow}, what is the Reynolds number below which the flow is exclusively laminar? (a) 500 (b) 2000 (c) 1000 (d) 10000 (e) 3000 Correct Answer: (a) or (b) depending on the question