Fluid Mechanics - Torque at hinge of closed vessel

In summary, if the water is stationary and the gate is at the top of the spout, then the torque needed to keep the gate closed is 9 times the weight of the water. If the water is flowing, then the height of the opening matters and not the shape of the spout.
  • #1
Aerospace
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The closed vessel contains water with an air pressure of 10 psi at the water surface. One side of the vessel contains a spout closed by a 6-inch diameter circular gate hinged along one side. Horizontal axis of the hinge is located 10 ft below the water surface. Determine the minimum torque that needs to be applied at the hinge to hold the gate shut.

Okay.
Here's what I am thinking, and please let me know if I am doing this correctly.

First, I'm trying to find the resultant Force = F. Here's where I am slightly confused. Do I take this body as a curved surface or not? because the gate is located at a spout which is circular. If not, then what I did was just

A = pi * r^2 = 9*pi in^2 = pi/16 ft^2
hc (vertical distance from fluid surface to centroid of area) = 10 ft
specific weight = 62.4 lb/ft^3

F = sp wt * hc * A = 122.52 lb

Torque (T) = F * radius = F * (3/12)ft = 30.63 lb-ft

Is that right?
 

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  • #2
Aerospace said:
The closed vessel contains water with an air pressure of 10 psi at the water surface. One side of the vessel contains a spout closed by a 6-inch diameter circular gate hinged along one side. Horizontal axis of the hinge is located 10 ft below the water surface. Determine the minimum torque that needs to be applied at the hinge to hold the gate shut.

Okay.
Here's what I am thinking, and please let me know if I am doing this correctly.

First, I'm trying to find the resultant Force = F. Here's where I am slightly confused. Do I take this body as a curved surface or not? because the gate is located at a spout which is circular. If not, then what I did was just

A = pi * r^2 = 9*pi in^2 = pi/16 ft^2
hc (vertical distance from fluid surface to centroid of area) = 10 ft
specific weight = 62.4 lb/ft^3

F = sp wt * hc * A = 122.52 lb

Torque (T) = F * radius = F * (3/12)ft = 30.63 lb-ft

Is that right?

The center of the gate is not exactly 10 feet below the surface. The hinge is 10 feet below the surface. The curvature of the spout makes no difference, but the pressure across the surface of the gate is not uniform. To find the torque due to the water accurately you would need to integrate the pressure times the moment arm over the surface of the gate. Since they give you the angle of the gate, I assume they want you to take the pressure variation into account. Even if you did not, the variation in the moment arm as you move away from the hinge would have to be considered.
 
  • #3
Calculate the velocity of efflux from the curved pipe opening using Bernoulli's Theorem. This water-flow will form a force at the circular gate trying to push it outwards, therefore equal and opposite torque is needed to counteract the torque due to water flow. The force due to water flow is given by [itex]dAv^2[/itex] where d is the density of water .The torque will be the moment of this force about the hinge of the circular gate.

BJ
 
  • #4
The above is ofcourse not the case if the water is supposed to be stationary.If you let the liquid flow which is the case, the height of the opening matters and not the shape of the spout.
 
Last edited:

What is fluid mechanics?

Fluid mechanics is a branch of physics that deals with the study of fluids (liquids and gases) and the forces that act on them.

What is torque at the hinge of a closed vessel?

Torque at the hinge of a closed vessel refers to the rotational force that is exerted on the vessel's hinge due to the pressure difference between the inside and outside of the vessel.

How is torque at the hinge of a closed vessel calculated?

To calculate the torque at the hinge of a closed vessel, you need to know the pressure difference between the inside and outside of the vessel, the distance from the hinge to the center of mass of the vessel, and the angle of the hinge. The formula for torque is torque = force x distance, so you can calculate the torque by multiplying the pressure difference by the distance and the sine of the angle.

What factors affect the torque at the hinge of a closed vessel?

The torque at the hinge of a closed vessel is affected by the pressure difference, the distance from the hinge to the center of mass of the vessel, and the angle of the hinge. It is also affected by the density and viscosity of the fluid, as well as the shape and size of the vessel.

Why is torque at the hinge of a closed vessel important?

Understanding the torque at the hinge of a closed vessel is important in various applications, such as designing pressure vessels and hydraulic systems. It also helps in predicting the stability and behavior of the vessel under different pressure conditions.

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