Deck 5: The Differential Forms of the Fundamental Laws

Question 1

A rectangular tank $80 \mathrm {~cm}$ high and $180 \mathrm {~cm}$ long is filled with water and pressurized to $20 \mathrm { kPa }$ at the top. If it is accelerated at the rate of $5 \mathrm {~m} / \mathrm { s } ^ { 2 }$ on a horizontal plane in the direction of its longer side, what is the highest pressure in the tank?

A) 49.1 kPa
B) 44.9 kPa
C) 41.2 kPa
D) 36.8 kPa

Answer 1

36.8 kPa

Question 2

If the U-tube of No. 4 is rotated about the right leg, what maximum rpm will result in the $20 ^ { \circ } \mathrm { C }$ water being thrown from the tube?

A) 741 rpm
B) 672 rpm
C) 569 rpm
D) 432 rpm

Answer 2

672 rpm

Question 3

The U-tube shown is rotated abou (A) $5.6 \mathrm { kPa }$
(B) $4.2 \mathrm { kPa }$
(C) $2.2 \mathrm { kPa }$
(D) $0.8 \mathrm { kPa }$ t the left vertical leg at 100

Answer 3

B
B
$4.2 \mathrm { kPa }$
The highest pressure occurs at the right-hand corner of the bottom where $r _ { 2 } = 0.2 \mathrm {~m}$ . Select $p _ { 1 } = 0$ at the top of the left leg. Using $\omega = 100 \times 2 \pi / 60 = 10.47 \mathrm { rad } / \mathrm { s }$ , Eq.2.6.4 provides

$p_{2}=\frac{1000}{2} 10.47^{2} \times 0.2^{2}-9810 \times(-0.2)=\underline{4154 \mathrm{~Pa}}$

Careful: Point 2 is at $( 0.2 , - 0.2 ) \mathrm { m }$ . (The units will work out if we use $\mathrm { kg } , \mathrm { N } , \mathrm { m }$ , and $\mathrm { s }$ as the units. Check them if you're uncertain. Angular velocity must be in rad/s, never rpm).

Question 4

The tank in Problem 1 has a small hole positioned in its top at the very rear of the tank which is accelerated at $a _ { x } = 5 \mathrm {~m} / \mathrm { s } ^ { 2 }$ in the direction of the longer side. The lowest pressure in the tank, which is filled with water, is nearest:

A) $12 \mathrm { kPa }$
B) $9 \mathrm { kPa }$
C) $- 9 \mathrm { kPa }$
D) $- 18 \mathrm { kPa }$

Question 5

The force acting on the bottom of the cylinder of Example 2.12 is nearest:

A) 55.6 N
B) 50.4 N
C) 45.2 N
D) 38.4 N rpm. The highest pressure in the U-tube is nearest: