Measurements of the liquid height upstream from an obstruction placed in an open-channel flow can be used to determine volume flow rate. (Such obstructions, designed and calibrated to measure rate of open-channel flow, are called weirs.) Assume the volume flow rate, Q, over a weir is a function of upstream height, h, gravity, g, and channel width, b. Use dimensional analysis to find the functional dependence of Q on the other variables.
Want to see the full answer?
Check out a sample textbook solutionChapter 7 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Degarmo's Materials And Processes In Manufacturing
Engineering Mechanics: Dynamics (14th Edition)
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
Engineering Mechanics: Statics
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
- The flow rate in a rectangular open channel can be measured by placing a plate along the channel as seen in the figure. This type of artifact is called "weir".The height of the water, H, above the ridge is referred to as "head" and can be used to determine the flow through the channel. Assume that flow Q is a function of H, channel width, b, and gravity, g.Determine a correct array of dimensionless variables for this problem.arrow_forwardA weir is an obstruction in a channel flow that can be calibratedto measure the flow rate, as in Fig. . The volumeflow Q varies with gravity g , weir width b into thepaper, and upstream water height H above the weir crest. Ifit is known that Q is proportional to b , use the pi theorem tofind a unique functional relationship Q ( g , b , H ).arrow_forward: The discharge pressure (P) of a gear pump (Fig. 3) is a function of flow rate (Q), gear diameter (D), fluid viscosity (µ) and gear angular speed (w). P = f (Q, D, H, 0). Use the pi theorem to rewrite this function in terms of dimensionless parameters. Suction Discharge Fig. 3: Gear pump P, Qarrow_forward
- A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density p, and viscosity u. Its center deflection & is assumed to be a function of all these variables. Part A-Rewrite this proposed function in dimensionless form.arrow_forwardA tiny aerosol particle of density pp and characteristic diameter Dp falls in air of density p and viscosity u . If the particle is small enough, the creeping flow approximation is valid, and the terminal settling speed of the particle V depends only on Dp, µ, gravitational constant g, and the density difference (pp - p). Use dimensional analysis to generate a relationship for Vas a function of the independent variables. Name any established dimensionless parameters that appear in your analysis.arrow_forwardForce F is applied at the tip of a cantilever beam of length L and moment of inertia I Fig. . The modulus of elasticity of the beam material is E. When the force is applied, the tip deflection of the beam is z d.Use dimensional analysis to generate a relationship for zd as a function of the independent variables. Name any established dimensionless parameters that appear in your analysisarrow_forward
- PROPAGATION OF ERROR You are tasked to supervise the design of 0.5MW wind turbine to be constructed in a Wind Farm in Pililla, Rizal. Suppose the design criteria are as follows: The air density as surveyed after 2 year period averaged at 1.225 kg / cubic meter. The sweeping diameter of the rotor blades is 125m, and the anemometer reading in the area amounts to 4.2m/s on a 2 year period of survey. What is the theoretical power output of the turbine assuming 100% efficiency of operation? Your answer must be in kW and in two decimal places with correct signs. In the previous problem, if the diameter measurement is off by 0.1m and the anemometer reading is also fluctuating by 0.05m/s and if the error measurement for theoretical power output must be limited to 3%, WHY OR WHY NOT should you accept the design? * Show complete solution in paper.arrow_forward1. The thrust of a marine propeller Fr depends on water density p, propeller diameter D, speed of advance through the water V, acceleration due to gravity g, the angular speed of the propeller w, the water pressure 2, and the water viscosity . You want to find a set of dimensionless variables on which the thrust coefficient depends. In other words CT = Fr pV2D² = fen (T₁, T₂, ...Tk) What is k? Explain. Find the 's on the right-hand-side of equation 1 if one of them HAS to be a Froude number gD/V.arrow_forward5.5 An automobile has a characteristic length and area of 8 ft and 60 ft, respectively. When tested in sea-level standard air, it has the following measured drag force versus speed: V, mi/h: 20 40 60 Drag, Ibf. 31 115 249 The same car travels in Colorado at 65 mi/h at an altitude of 3500 m. Using dimensional analysis, estimate (a) its drag force and (b) the horsepower required to overcome air drag.arrow_forward
- 5.28 A simply supported beam of diameter D, length L, and modulus of elasticity E is subjected to a fluid crossflow of velocity V, density e, and viscosity u. Its center deflection d is assumed to be a function of all these variables. (a) Rewrite this proposed function in dimensionless form. (b) Suppose it is known that ô is independent of u, inversely proportional to E, and dependent only upon pl, notp and V separately. Simplify the dimensionless function accordingly.arrow_forwardWhen a fluid flows slowly past a vertical plate of height h and width b, pressure develops on the face of the plate. Assume that the pressure, p, at the midpoint of the plate is a function of plate height and width, the approach velocity V, and the fluid viscosity u and fluid density p. Make use of dimensional analysis to determine how the pressure, p will be formed with a dimensionless group. (Take b, V. p as repeating variables). Select one: O a. n1 = p /V² p O b. n1 = p/Ve O c.n1 = p/Vp? O d. 11 = p/V² p²arrow_forward7. A model propeller of diameter D = 0.8 m is tested in a wind tunnel at pressure and temperature conditions corresponding to an air density p = 1.2 kg/m³. With the propeller spinning at 2000 rpm (revolutions per minute), the thrust T was measured at several forward velocities V: = V (m/s) Thrust (N) 0 10 20 30 300 275 210 100 (a) Use dimensional analysis to find the dimensionless parameters that govern this data. (b) Using the data, predict the thrust you would expect for a full-scale propeller of diameter D₁ 3.0 m, spinning at 1500 rpm (revolutions per minute), at a forward velocity of 45 m/s, and at high-altitude conditions where the air density is 0.6 kg/m³. You may need to interpolate or extrapolate the experimental data. =arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning