It is desired to design a cup anemometer for wind speed, similar to Fig. P7.91, with a more sophisticated approach than the “average-torque” method of Prob. P7.91. The design should achieve an approximately linear relation between wind velocity and rotation rate in the range 20 < U < 40 mi/h, and the anemometer should rotate at about 6 r/s at U = 30 mi/h. All speci?cations—cup diameter D, rod length L, rod diameter d, the bearing type, and all materials—are to be selected through your analysis. Make suitable assumptions about the instantaneous drag of the cups and rods at any given angle
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Chapter 7 Solutions
FLUID MECHANICS W/ONLINE ACCESS CODE
- Pipelines are cleaned by pushing through them a closefitting cylinder called a pig . The name comes from thesquealing noise it makes sliding along. Reference 50describes a new nontoxic pig, driven by compressed air, forcleaning cosmetic and beverage pipes. Suppose the pigdiameter is 5-15/16 in and its length 26 in. It cleans a6-in-diameter pipe at a speed of 1.2 m/s. If the clearance isfi lled with glycerin at 20 8 C, what pressure difference, inpascals, is needed to drive the pig? Assume a linear velocityprofi le in the oil and neglect air drag.arrow_forwardAn instrument popular in the water supply industry,sketched in Fig., is the single jet water meter.(a) How does it work? (b) What do you think a typicalcalibration curve would look like? (c) Can you cite furtherdetails, for example, reliability, head loss, cost ?arrow_forwardThe drag of a sonar transducer is to be predicted, based on wind (Air) tunnel test data. The prototype is 1.5 m diameter sphere, is to be towed at 4.3 m/s in seawater. The model is 0.2 m diameter. Take: Air density = 1.2 kg/m, Air dynamic viscosity = 1.81 x 10$ Pa. s, seawater density = 1000 kg/m, seawater dynamic viscosity 1.813x 10 Pa s, If the drag of the model at these test conditions is 9.5 N, estimate the drag of the prototype in (N).arrow_forward
- 1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?arrow_forward(a) You would like to measure wind speed with a cup anemometer on a sailboat trip across the Atlantic Ocean. The measure of the rotational speed of the axle of the device has a precision of +/-0.2 rotations/s and was calibrated in a steady wind-tunnel flow at 20m/s with 10 rotations/s. Define for the below-given situations, 1 to 4, the type of error (random or systematic) and explain how to overcome or reduce this error. 1 Bearing of the axle is old 2 Turbulent flow 3 Icing on the cups 4 Strong tumbling of the sailboat You would like to use it for a measure of the in-cabin air flow a quiet environment. Discuss why the measurement system is not well posed for this purpose.arrow_forwardApply the necessary conversion factors to prove the relationship between dimensionless turbine specific speed and customary U.S. turbine specific speed, NSt = 43.46NSt, US. Note that we assume water as the fluid and standard earth gravity.arrow_forward
- Q.5 A plate 1 mm distance from a fixed plate, is moving at 500 mm/s by a force induces a 2 shear stress of 0.3 kg(f)/m. The kinematic viscosity of the fluid (mass density 1000 kg/ 3. m) flowing between two plates (in Stokes) isarrow_forwardA certain garden hose is advertised to be able to deliver 550 gallons of water per hour. If the hose if 50 feet long and has an inside diameter of 5/8 inch, estimate the water pressure necessary to deliver this much water, assuming laminar flow and viscosity at 1.002 x 10-3 kg/(m-s)arrow_forwardWall friction τ w , for turbulent flow at velocity U in apipe of diameter D , was correlated, in 1911, with a dimensionless correlation by Ludwig Prandtl’s studentH. Blasius: Suppose that ( ρ , U , μ , τ w ) were all known and it was desiredto find the unknown velocity U . Rearrange and rewritethe formula so that U can be immediately calculated.arrow_forward
- Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?arrow_forwardAir with density of 1.225 kg/m^3 and viscosity of 1.789 x 10^-5 kg/m-s flows in a wind tunnel, the wind tunnel spped is measured with Pitot tube probe. For a certain run, the stagantion pressure is measured to be 472.6 Pa gage and the statric pressure is 15.43 Pa gage. Calculate the wind tunnel speed. (WITH FREE BODY DIAGRAM) CHOICES: a.17. 3 m/s b.18. 3 m/s c.19. 3 m/s d.16.3 m/sarrow_forwardConsider laminar flow through a long section of pipe, as in Fig. For laminar flow it turns out that wall roughness is not a relevant parameter unless ? is very large. The volume flow rate V· through the pipe is a function of pipe diameter D, fluid viscosity ? , and axial pressure gradient dP/dx. If pipe diameter is doubled, all else being equal, by what factor will volume flow rate increase? Use dimensional analysis.arrow_forward
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