The depth of the centre of pressure on a vertical rectangular gate ( 4m wide , 3m high) with water up to top surface (a) 1m. (b) 1.5m. (c) 2m (d) 2.5m?

Question

Answer

Calculation of Depth of Centre of Pressure on a Vertical Rectangular Gate

Given:

Width of gate (w) = 4m

Height of gate (h) = 3m

Case 1: Water level is at 1m

The depth of the centre of pressure can be calculated using the formula:

Depth of Centre of Pressure = h/2 + I/(h*γ)

where,

h = height of gate

I = moment of inertia of the gate section about an axis passing through the centroid

γ = unit weight of water

For a rectangular section, the moment of inertia can be calculated as:

I = (w*h^3)/12

Substituting the given values, we get:

I = (4*3^3)/12 = 27m^4

Substituting the values in the formula, we get:

Depth of Centre of Pressure = 3/2 + 27/(3*9810) = 1.76m

Case 2: Water level is at 1.5m

Using the same formula as above, we get:

Depth of Centre of Pressure = 3/2 + 27/(4.5*9810) = 1.93m

Case 3: Water level is at 2m

Using the same formula as above, we get:

Depth of Centre of Pressure = 3/2 + 27/(6*9810) = 2.09m

Case 4: Water level is at 2.5m

Using the same formula as above, we get:

Depth of Centre of Pressure = 3/2 + 27/(7.5*9810) = 2.22m

Therefore, the depth of centre of pressure on a vertical rectangular gate varies with the water level and can be calculated using the above formula. As the water level increases, the depth of centre of pressure also increases.

Answer

1.5

Answer

2

Similar Civil Engineering (CE) Doubts

When the water surface coincides with the top edge of a rectangular vertical gate 40 m (wid e) x 3 m (deep), then the depth of centre of pressure is

A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5 m and 6.0 m respectively below the free surface. The position of centre of pressure below the free surface will be at a distance of

A longitudinal rectangular surface is hanged into the water such that its top and bottom points are at depth of 1.5 m and 6.0 m respectively. The depth of center of pressure (m) from the top surface is _____.

A rectangular plane surface of width 2 m and height 3 m is placed vertically in water. What will be the location of center of pressure of the surface when its upper edge is horizontal and lies 2.5 m below the free surface of water?

A vertical rectangular plane surface is submerged in water such that its top and bottom surfaces are 1.5m and 6.0m respectively below the free surface the position of the centre of pressure below the free surface?

Top Courses for Civil Engineering (CE)View all

General Aptitude for GATE

GATE Civil Engineering (CE) 2025 Mock Test Series

Fluid Mechanics for Civil Engineering

General Awareness & Knowledge

Topicwise Question Bank for Civil Engineering

Top Courses for Civil Engineering (CE)

Top Courses for Civil Engineering (CE)

Suggested Free Tests

Related Content

Mock Test Series

Subject-wise Courses

Subject-wise Courses

Other Engg Branches

Company