Solution :
Given data is :
Density of the milk in the tank, ![$\rho = 1020 \ kg/m^3$](https://tex.z-dn.net/?f=%24%5Crho%20%3D%201020%20%5C%20kg%2Fm%5E3%24)
Length of the tank, x = 9 m
Height of the tank, z = 3 m
Acceleration of the tank, ![$a_x = 2.5 \ m/s^2$](https://tex.z-dn.net/?f=%24a_x%20%3D%202.5%20%5C%20m%2Fs%5E2%24)
Therefore, the pressure difference between the two points is given by :
![$P_2-P_1 = -\rho a_x x - \rho(g+a)z$](https://tex.z-dn.net/?f=%24P_2-P_1%20%3D%20-%5Crho%20a_x%20x%20-%20%5Crho%28g%2Ba%29z%24)
Since the tank is completely filled with milk, the vertical acceleration is ![$a_z = 0$](https://tex.z-dn.net/?f=%24a_z%20%3D%200%24)
![$P_2-P_1 = -\rho a_x x- \rho g z$](https://tex.z-dn.net/?f=%24P_2-P_1%20%3D%20-%5Crho%20a_x%20x-%20%5Crho%20g%20z%24)
Therefore substituting, we get
![$P_2-P_1=-(1020 \times 2.5 \times 7) - (1020 \times 9.81 \times 3)$](https://tex.z-dn.net/?f=%24P_2-P_1%3D-%281020%20%5Ctimes%202.5%20%5Ctimes%207%29%20-%20%281020%20%5Ctimes%209.81%20%5Ctimes%203%29%24)
![$=-17850 - 30018.6$](https://tex.z-dn.net/?f=%24%3D-17850%20-%2030018.6%24)
![$=-47868.6 \ Pa$](https://tex.z-dn.net/?f=%24%3D-47868.6%20%5C%20Pa%24)
![$=-47.868 \ kPa$](https://tex.z-dn.net/?f=%24%3D-47.868%20%5C%20kPa%24)
Therefore the maximum pressure difference in the tank is Δp = 47.87 kPa and is located at the bottom of the tank.
Answer:
it can cause huricans and flooding
Explanation:
Storm surge is the rising of the sea level due to the low pressure, high winds, and high waves associated with a hurricane as it makes landfall. The storm surge can cause significant flooding and cost people their lives if they're caught unexpected
Answer:
Part a: When the road is level, the minimum stopping sight distance is 563.36 ft.
Part b: When the road has a maximum grade of 4%, the minimum stopping sight distance is 528.19 ft.
Explanation:
Part a
When Road is Level
The stopping sight distance is given as
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D)
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is this case is 0 as the road is level
Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0)}\\SSD=220.5 +342.86 ft\\SSD=563.36 ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35-0%29%7D%5C%5CSSD%3D220.5%20%2B342.86%20ft%5C%5CSSD%3D563.36%20ft)
So the minimum stopping sight distance is 563.36 ft.
Part b
When Road has a maximum grade of 4%
The stopping sight distance is given as
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D)
Here
- SSD is the stopping sight distance which is to be calculated.
- u is the speed which is given as 60 mi/hr
- t is the perception-reaction time given as 2.5 sec.
- a/g is the ratio of deceleration of the body w.r.t gravitational acceleration, it is estimated as 0.35.
- G is the grade of the road, which is given as 4% now this can be either downgrade or upgrade
For upgrade of 4%, Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35+0.04)}\\SSD=220.5 +307.69 ft\\SSD=528.19 ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35%2B0.04%29%7D%5C%5CSSD%3D220.5%20%2B307.69%20ft%5C%5CSSD%3D528.19%20ft)
<em>So the minimum stopping sight distance for a road with 4% upgrade is 528.19 ft.</em>
For downgrade of 4%, Substituting values
![SSD=1.47 ut +\frac{u^2}{30 (\frac{a}{g} \pm G)}\\SSD=1.47 \times 60 \times 2.5 +\frac{60^2}{30 \times (0.35-0.04)}\\SSD=220.5 +387.09 ft\\SSD=607.59ft](https://tex.z-dn.net/?f=SSD%3D1.47%20ut%20%2B%5Cfrac%7Bu%5E2%7D%7B30%20%28%5Cfrac%7Ba%7D%7Bg%7D%20%5Cpm%20G%29%7D%5C%5CSSD%3D1.47%20%5Ctimes%2060%20%5Ctimes%202.5%20%2B%5Cfrac%7B60%5E2%7D%7B30%20%5Ctimes%20%280.35-0.04%29%7D%5C%5CSSD%3D220.5%20%2B387.09%20ft%5C%5CSSD%3D607.59ft)
<em>So the minimum stopping sight distance for a road with 4% downgrade is 607.59 ft.</em>
As the minimum distance is required for the 4% grade road, so the solution is 528.19 ft.
Answer:
(a) t = 1.14 s
(b) h = 0.82 m
(c) vf = 7.17 m/s
Explanation:
(b)
Considering the upward motion, we apply the third equation of motion:
![2gh = v_f^2 - v_i^2](https://tex.z-dn.net/?f=2gh%20%3D%20v_f%5E2%20-%20v_i%5E2)
where,
g = - 9.8 m/s² (-ve sign for upward motion)
h = max height reached = ?
vf = final speed = 0 m/s
vi = initial speed = 4 m/s
Therefore,
![(2)(9.8\ m/s^2)h = (0\ m/s)^2-(4\ m/s)^2\\](https://tex.z-dn.net/?f=%282%29%289.8%5C%20m%2Fs%5E2%29h%20%3D%20%280%5C%20m%2Fs%29%5E2-%284%5C%20m%2Fs%29%5E2%5C%5C)
<u>h = 0.82 m</u>
Now, for the time in air during upward motion we use first equation of motion:
![v_f = v_i + gt_1\\0\ m/s = 4\ m/s + (-9.8\ m/s^2)t_1\\t_1 = 0.41\ s](https://tex.z-dn.net/?f=v_f%20%3D%20v_i%20%2B%20gt_1%5C%5C0%5C%20m%2Fs%20%3D%204%5C%20m%2Fs%20%2B%20%28-9.8%5C%20m%2Fs%5E2%29t_1%5C%5Ct_1%20%3D%200.41%5C%20s)
(c)
Now we will consider the downward motion and use the third equation of motion:
![2gh = v_f^2-v_i^2](https://tex.z-dn.net/?f=2gh%20%3D%20v_f%5E2-v_i%5E2)
where,
h = total height = 0.82 m + 1.8 m = 2.62 m
vi = initial speed = 0 m/s
g = 9.8 m/s²
vf = final speed = ?
Therefore,
![2(9.8\ m/s^2)(2.62\ m) = v_f^2 - (0\ m/s)^2\\](https://tex.z-dn.net/?f=2%289.8%5C%20m%2Fs%5E2%29%282.62%5C%20m%29%20%3D%20v_f%5E2%20-%20%280%5C%20m%2Fs%29%5E2%5C%5C)
<u>vf = 7.17 m/s</u>
Now, for the time in air during downward motion we use the first equation of motion:
![v_f = v_i + gt_1\\7.17\ m/s = 0\ m/s + (9.8\ m/s^2)t_2\\t_2 = 0.73\ s](https://tex.z-dn.net/?f=v_f%20%3D%20v_i%20%2B%20gt_1%5C%5C7.17%5C%20m%2Fs%20%3D%200%5C%20m%2Fs%20%2B%20%289.8%5C%20m%2Fs%5E2%29t_2%5C%5Ct_2%20%3D%200.73%5C%20s)
(a)
Total Time of Flight = t = t₁ + t₂
t = 0.41 s + 0.73 s
<u>t = 1.14 s</u>