Answer:
Stat PVC = Stat(82+98.5)
Stat PVT = Stat(59+71.5)
Explanation
PVI = 71 + 35
Let G1 = Grade 1; G2 = Grade 2
G1 = +2.1% ; G2 = -3.4%
Highest point of curve at station = 74 + 10
General equation of a curve:
![y = ax^{2} +bx+c\\dy/dx=2ax+b\\](https://tex.z-dn.net/?f=y%20%3D%20ax%5E%7B2%7D%20%2Bbx%2Bc%5C%5Cdy%2Fdx%3D2ax%2Bb%5C%5C)
At highest point of the curve ![dy/dx=o](https://tex.z-dn.net/?f=dy%2Fdx%3Do)
![2ax+b=0\\x=-b/2a\\x=G1L/(G2-G1)\\x=L/2 +(stat 74+10)-(stat 71+35)\\x=L/2 + 275](https://tex.z-dn.net/?f=2ax%2Bb%3D0%5C%5Cx%3D-b%2F2a%5C%5Cx%3DG1L%2F%28G2-G1%29%5C%5Cx%3DL%2F2%20%2B%28stat%2074%2B10%29-%28stat%2071%2B35%29%5C%5Cx%3DL%2F2%20%2B%20275)
![-G1L/(G2-G1) = (L/2 + 275)/100\\L = -2327 ft\\Station PVC = Stat(71+35)+(-2327/2)\\\\Stat PVC = 7135-1163.5\\Stat PVC = Stat(82+98.5)\\](https://tex.z-dn.net/?f=-G1L%2F%28G2-G1%29%20%3D%20%28L%2F2%20%2B%20275%29%2F100%5C%5CL%20%3D%20-2327%20ft%5C%5CStation%20PVC%20%3D%20Stat%2871%2B35%29%2B%28-2327%2F2%29%5C%5C%5C%5CStat%20PVC%20%3D%207135-1163.5%5C%5CStat%20PVC%20%3D%20Stat%2882%2B98.5%29%5C%5C)
Station PVT
![Station PVT = Stat PVI + (L/2)\\Station PVT = Stat(71+35)+(-2327/2)\\Station PVT = 7135-1163.5\\Stat PVT = Stat(59+71.5)](https://tex.z-dn.net/?f=Station%20PVT%20%3D%20Stat%20PVI%20%2B%20%28L%2F2%29%5C%5CStation%20PVT%20%3D%20Stat%2871%2B35%29%2B%28-2327%2F2%29%5C%5CStation%20PVT%20%3D%207135-1163.5%5C%5CStat%20PVT%20%3D%20Stat%2859%2B71.5%29)
Answer:
The flux (volume of water per unit time) through the hoop will also double.
Explanation:
The flux = volume of water per unit time = flow rate of water through the hoop.
The Flow rate of water through the hoop is proportional to the area of the hoop, and the velocity of the water through the hoop.
This means that
Flow rate = AV
where A is the area of the hoop
V is the velocity of the water through the hoop
This flow rate = volume of water per unit time = Δv/Δt =Q
From all the above statements, we can say
Q = AV
From the equation, if we double the area, and the velocity of the stream of water through the hoop does not change, then, the volume of water per unit time will also double or we can say increases by a factor of 2