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Exam2 - Problems (2) 1

The document outlines problems related to fluid mechanics, including calculations for jet velocity, pressure, and anchoring force in a nozzle, flow rate through a capillary tube, velocity distribution in a laminar film on an inclined plane, and vortex shedding from bluff cylinders. It provides specific parameters such as fluid properties and dimensions for each scenario. The problems require applying principles of fluid dynamics and dimensional analysis.

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70 views2 pages

Exam2 - Problems (2) 1

The document outlines problems related to fluid mechanics, including calculations for jet velocity, pressure, and anchoring force in a nozzle, flow rate through a capillary tube, velocity distribution in a laminar film on an inclined plane, and vortex shedding from bluff cylinders. It provides specific parameters such as fluid properties and dimensions for each scenario. The problems require applying principles of fluid dynamics and dimensional analysis.

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ali.elturki
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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ENGR:2510 Mechanics of Fluids and Transport Fall 2015

November 16, 2015

1. Water flows steadily through the nozzle shown in Fig. 1, discharging to atmosphere. Calculate
(a) the jet velocity V2 at the nozzle end, (b) the pressure p1 at the flanged joint, and (c) the
horizontal component of the anchoring force Fx to keep the nozzle in place. The elevation
difference is 12 in. and no loss between the flanged joint and the nozzle end (i.e., between
sections 1 and 2). Use ρ = 1.94 slugs/ft3 and γ = 62.4 lb/ft3 for water and g = 32.2 ft/s2.

Figure 1

2. A capillary tube of inside diameter d = 6 mm connects tank A and open container B as shown in
Fig. 2. The liquid in A, B, and capillary CD is water having a specific weight γ = 9,780 N/m3 and a
viscosity of µ = 0.0008 N⋅s/m2. The pressure pA = 34.5 kPa gage. Neglecting the minor losses at C
and D, determine the flow rate Q through the capillary tube. Assume laminar flow from A to B
and use hf = 32µLV/γd2 for the friction loss, where V is the water velocity through the capillary
tube.

Figure 2
ENGR:2510 Mechanics of Fluids and Transport Fall 2015
November 16, 2015

3. A viscous liquid flows down an inclined plane surface in a steady, fully developed laminar film of
thickness h and width b (out of the paper) as shown in Fig. 3. A useful approximation of the flow
is

𝑑𝑑2 𝑢𝑢
𝜇𝜇 = −𝜌𝜌g 𝑥𝑥
𝑑𝑑𝑦𝑦 2

where, g 𝑥𝑥 = g⋅sinθ is the x-component of the gravity acceleration. (a) Derive an expression for
the velocity distribution 𝑢𝑢(𝑦𝑦) by integrating the given equation then applying the free-shear
(i.e., 𝑑𝑑𝑑𝑑⁄𝑑𝑑𝑑𝑑 = 0) boundary condition at the top and the no-slip boundary condition at the
bottom. (b) If the liquid is SAE 30 oil at 15.6°C (ρ = 912 kg/m3 and µ = 0.38 N⋅s/m2) and h = 1
ℎ
mm, b = 1 m, and θ = 15°, find the volume flow rate, 𝑄𝑄 = ∫0 𝑢𝑢(𝑦𝑦)𝑏𝑏𝑏𝑏𝑏𝑏.

Figure 3

4. In some speed ranges, vortices are shed from the rear of bluff cylinders placed across a flow.
The vortices alternately leave the top and bottom of the cylinder, as shown in Fig. 4. The vortex
shedding frequency, f, is thought to dependent on fluid density, ρ, and viscosity, µ, cylinder
diameter, d, and free-stream velocity, V. (a) Use dimensional analysis to develop a functional
relationship for f. (b) Vortex shedding occurs in standard air on two cylinders with diameters 𝑑𝑑𝑚𝑚
and 𝑑𝑑𝑝𝑝 , respectively. If the diameter ratio is dp/dm = 2, determine the velocity ratio, Vp/Vm, for
dynamic similarity, and the ratio of vortex shedding frequencies, fp/fm. For part (a), use the MLT
unit system.

Figure 4

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