A gate in an irrigation canal is constructed in the form of a trapezoid 6?m wide

Question

A gate in an irrigation canal is constructed in the form of a trapezoid 6?m wide at the bottom, 60?m wide at the top, and 2?m high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate.

Note that your answer should be in Newtons, and use g = 9.8 m/s2. A gate in an irrigation canal is constructed in the form of a trapezoid 6?m wide at the bottom, 60?m wide at the top, and 2?m high. It is placed vertically in the canal so that the water just covers the gate. Find the hydrostatic force on one side of the gate.

Note that your answer should be in Newtons, and use g = 9.8 m/s2.

Explanation / Answer

p = sp.wt.* depth = 62.4*depth in ft. (for fresh water)

A) F=p*Area=62.4*9*80 =

B) Let x be depth. Then

F=int(62.4*x*10dx) from 0 to 9 =

C) Assuming the gate is at the bottom of the tank, let y= distance from bottom. Then integration by strips parallel to bottom gives

F=int[62.4*(9-y)(2-y)dy] from 0 to 1 =

Calculations left to student.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.