Assignment-IMeasurements in Fluid Mechanics

AE611 & AE611AI Semester 2014-15 (July –Nov)

Q1.

Q2. A pipe connecting two reservoirs, as in Fig.P2 below, contains a thin-plate orifice. For water flow at 20C, estimate (a) the volume flow through the pipe and(b) the pressure drop across the orifice plate.

Fig. P2

Q3.Gasoline at 20C flows at 0.06 m3/s through a 15-cm pipe and is metered by a 9-cm-diameter long-radius flow nozzle. What is the expected pressure drop across the nozzle? State any method of measuring this pressure with its accuracy of measurement.

Q4. Consider a flow nozzle installation in a pipe. Apply the basic equations to the control volume indicated, to show that permanent head loss across the meter can be expressed in dimensionless form, as the head loss coefficient,

Q5. In a laboratory experiment, air at 20C flows from a large tank through a 2-cm-diameter smooth pipe into a sea-level atmosphere, as shown in Fig. P5. The flow is metered by a long-radius nozzle of 1-cm diameter, using a manometer with Meriam red oil (SG 0.827). The pipe is 8 m long. The measurements of tank pressure and manometer height are as follows:

Fig. P5

Use this data to calculate the flow rates Q and Reynolds numbers ReD and make a plot of measured flow rate versus tank pressure. Is the flow laminar or turbulent? Compare the

data with theoretical results obtained from the Moody chart, including minor losses. Discuss the results.

Q6.

Air flows at high speed through a Herschel venturi monitored by a mercury manometer, as shown in Fig.p6. The upstream conditions are 150 kPa and 80C. If h 37 cm, estimate the mass flow in kg/s.[HINT: The flow is compressible and use compressible flow expansion factor.]

Fig. P6

Q7 To estimate the error in temperature correction due to the assumption of lapse rate say the barometric equation is re-casted by combining all constants into one term as,

z = K T Δ(ln p)Now suppose the average temperature for the column of air is calculated using two different lapse rates, ΔT1 and ΔT2, and found to be T1 and T2 respectively. If z is the true height, and z1 and z2 are estimated based on T1 and T2 respectively, show,

z1 – z2 = (ΔT1 – ΔT2).z2/2000T2

If ΔT1 is 10K per 1000m, ΔT2 is 6.5K per 1000m and T2 is 283K then find the error, z1–z2 for z=500m, 1000m and 1500m. Discuss the implication of this result in any two particular applications.

Problems are from Holman’s 7th edition book

Q8-17. 2.11, 2.15, 2.29, 2.30, 2.40, 2.47 2.48, 3.14, 3.15 & 3.20.

Q18. (a) Define the following terms and estimate the same for the given input (P) output (V) data below. (i) Sensitivity, (ii) Resolution and threshold (iii) Non-linearity and (iv) Differential non-linearity. Note, that V does not vary linearly with P. (b) If the input data is the measured low pressure (P) in kPa and output (V) is in mv from the transducer, and the data is also a measure of pressure of 0.16kPa, determine the accuracy and precision of the measurement.p = [0.1000 0.1200 0.1400 0.1600 0.1800 0.2000]V = [0.0100 0.0144 0.0196 0.0256 0.0324 0.0400]

Q19. Determine frequency response of a 2nd order system with the input as (i) linear variation with time and (ii) sinusoidal variation of time.

Q20. Define gauge factor of a strain gauge. A resistance strain gauge with resistance R = 80Ω and gauge facto 2.0 is used in force/strain measurement bridge such that all resistance are equal to 80Ω. The input voltage to the bridge is 4V. Find the output voltage for strain of 100μm/m. If four such strain gauges are used in a balance for measuring (i) a lift force of 1kgf and (ii) Moment of 0.1N-m, sketch the balance configuration and corresponding Wheatstone bridge circuit and find the output voltage. Assume all other quantities required to a reasonable value.

Q21. Derive the time constant for a hotwire in reference to its response equation. In experiments how this time constant is determined.

Q22. (a) Derive the energy balance equation of a hotwire to find the variation of temperature of a hotwire along its length. (b) Is the frequency response of a hotwire is determined from a second order equation? Explain from part (a) of this question. (c) Explain any one method of using hotwire for measuring reverse flow velocity.

Background Problems:

Q23. In a flow field velocity vector (i) V = (y+kt)i + (-x-kt)j. where, k is constant. Find a) the equation of a streamline passing through point A(x=0 y =1) b) the equation of the pathline of a particle passing through A at t =0. c) the equation of a streakline at t =T when dye is injected at A.d) If k = 0, calculate the same as (a) (b) (c). Discuss the implications of the results.

Q24.