Deck 2: Fluid Statics

Question 1

The specific weight of air at 5 km is nearest: (A) $6.14 \mathrm {~N} / \mathrm { m } ^ { 3 }$
(B) $6.66 \mathrm {~N} / \mathrm { m } ^ { 3 }$
(C) $7.26 \mathrm {~N} / \mathrm { m } ^ { 3 }$
(D) $8.22 \mathrm {~N} / \mathrm { m } ^ { 3 }$

Answer 1

C C
$7.26 \mathrm {~N} / \mathrm { m } ^ { 3 }$
The density is found in Table B.3 in the Appendix. Using a straight-line interpolation
$$\rho = 0.8194 - \frac { 0.8194 - 0.6602 } { 2 } = 0.7398 \text { or } 0.740 \mathrm {~kg} / \mathrm { m } ^ { 3 }$$
The interpolation will result in less accuracy so 4 significant digits is not appropriate. The specific weight is then, using Eq.1.5.1,
$$\gamma = \rho g = 0.740 \times 9.81 = \underline { 7.26 \mathrm {~N} / \mathrm { m } ^ { 3 } }$$

Question 2

Two clean, glass plates spaced $0.2 \mathrm {~mm}$ apart are placed in $20 ^ { \circ } \mathrm { C }$ water. How far up the plates will the water climb if the contact angle is $0 ^ { \circ }$ ?
(A) 75 mm
(B) 70 mm
(C) 65 mm
(D) 60 mm

Answer 2

A
A
$75 \mathrm {~mm}$
A free-body of the water between the plates would appear as in Fig. $1.10$ with $\beta = 0 ^ { \circ }$ . Summing forces provides
$$\begin{array} { c } \sigma \times 2 L = \gamma \times V = \gamma t L h \quad \text { or } 0.0736 \times 2 L = 9810 \times 0.0002 \mathrm { Lh } \\\therefore h = 0.0750 \mathrm {~m} \text { or } \underline { 75 \mathrm {~mm} }\end{array}$$

Question 3

Thunder is heard $2.2$ seconds after Lightning is observed in Arizona when the temperature is $50 ^ { \circ } \mathrm { C }$ . The best estimate of how far away the lightning struck is nearest:

A) 820 m
B) 790 m
C) 730 m
D) 650 m

Answer 3

790 m

Question 4

The specific gravity of an unknown liquid is known to be 1.26. The liquid is most likely:

A) Glycerin
B) Carbon tetrachloride
C) Mercury
D) Water

Question 5

A farmer is applying compressed nitrogen to a field from a tank originally at $800 \mathrm { kPa }$ . The temperature of the nitrogen as it leaves the tank is approximately:
(A) $- 140 ^ { \circ } \mathrm { C }$
(B) $- 120 ^ { \circ } \mathrm { C }$
(C) $- 100 ^ { \circ } \mathrm { C }$
(D) $- 80 ^ { \circ } \mathrm { C }$

Question 6

Estimate the torque needed to rotate the inner cylinder at $1000 \mathrm { rpm }$ if SAE-30 oil at $40 ^ { \circ } \mathrm { C }$ fills the gap. Assume a linear velocity distribution in the gap. Neglect end effects.


(A) $16.0 \mathrm {~N} \cdot \mathrm { m }$
(B) $16.9 \mathrm {~N} \cdot \mathrm { m }$
(C) $18.8 \mathrm {~N} \cdot \mathrm { m }$
(D) $20.2 \mathrm {~N} \cdot \mathrm { m }$
$60 - \mathrm { cm }$ long concentric cylinders