Safety Valve Calculations

Among the most frequent questions asked in an engineer’s examination are those relating to the safety valves of boilers.

These questions may be easily answered from a study of the following:

The safety valve is a device for relieving the boiler of steam after it has reached a certain pressure.

This it accomplishes by letting the steam escape after it has reached the required pressure.

At what pressure the safety valve will blow off depends upon the position of the weight on the safety valve lever.

The calculations referring to this part of the subject are, finding how much weight will be required to be placed at a given point on the lever, in order, with a given sized valve, to blow off at a given pressure.

Finding the position on the lever of a given amount of weight, in order to blow off at a certain pressure.

Finding, with a given sized valve and a given weight, how to mark off the lever and where the notches must be cut for given pressures.

In each of these calculations there are three elements: first, the area of the valve and the steam pressure, which constitute the effect of acting to lift the valve; second, the amount of the weight and its position upon the lever, which acts to keep the valve closed; and third, the weight of the lever and of the valve, which act to keep the valve closed.

In Fig. 3357 we have a drawing of a safety valve shown in section, and if there was no weight upon the lever, the pressure of steam the valve would hold in the boiler would be that due to the weight of the valve and of the lever upon the valve.

To find out how much this would be, we would have to put the valve itself and the pin a on a pair of scales and weigh them.

Then put a piece of string through the hole at a in the lever, and see how much it weighed when suspended from that point.

Suppose the valve and pin to weigh 2 lbs. and the lever (suspended by the string) 10, and the total will be 12 lbs.

Next we find the area of the valve, and suppose this to be 8 square inches; then we may find how much pressure the valve would keep in the boiler, by dividing the area of the valve into the weight holding the valve down, thus:

Lbs.

Weight of valve and pin, 2

„ „ lever, 10

Area of valve, 8 ) 12

Pressure the valve would hold, 1 .5 lbs.

The area of the valve is that part of its face receiving the steam pressure when the valve is seated, so that if the smallest part of the valve diameter is equal to the diameter of the seat bore, the diameter from which the valve area is to be calculated will be that denoted by d in the figure, and cannot in any case be less than this. But if the smallest end of the valve cone is of larger diameter than the smallest end of the seat cone (which should not, but might be the case), then it is the smallest diameter of valve cone that must be taken in calculating the area, because that is the area the steam will press against.

Now suppose we rest a 20 lb. weight on the top of the valve that is on the point denoted by i, and there will be 32 lbs. holding the valve down, thus, weight of valve 2 lbs., of lever 10, and weight added, 20 lbs., and to find how much pressure this would hold in the boiler, we divide it by the valve area, thus:

Weight on valve.

Valve area = 8 ) 32

4 = pressure valve will hold.

But suppose we put the weight on the lever, in the position shown in the figure, which is six times as far from the fulcrum f of the lever as the valve is, and its effect on the valve will be six times as great as it would if placed directly upon the valve, so that leaving the weight of the valve and of the lever out of the question (as is commonly done in engineers’ examinations), we may find out what pressure the valve will hold, as follows:

Rule.—Divide the length of the lever by the distance from the centre of the valve to the centre of the fulcrum. Multiply by the amount of the weight in lbs., and divide by the area of the valve.

Example.—The area of the valve is 8 inches, the distance from the centre of the fulcrum to the centre of the valve is 4 inches, and the distance from the fulcrum to the point of suspension of the weight 24 inches, the weight is 40 lbs., what pressure will the valve hold?

Length of lever.

From fulcrum to valve, 4 ) 24

6

4 0 amount of weight.

Area of valve, 8 ) 24 0

3 0

Lbs. per square inch the valve will hold = 30.

The philosophy of this is clear enough when we consider that as the weight is six times as far from the fulcrum as the valve is, and each 1 lb. of weight will press with a force of 6 lbs. on the valve, hence the 40 lbs. will press 240 lbs. on the valve, and as the valve has 8 square inches, the 240 becomes 30 lbs. for each inch of area.

Example.—The area of a safety valve is 8 inches, the distance from the fulcrum to the valve is 4 inches, and the weight is 40 lbs., how far must the weight be from the fulcrum to hold in the boiler a pressure of 30 lbs. per square inch?

In lbs.

From fulcrum to valve, 4 ) 4 0 amount of weight.

1 0

Area of valve, 8 square inches.

Pressure required, 3 0

10 ) 24 0

2 4

Answer = 24 inches from the fulcrum.

Example.—The diameter of a safety valve is 4 inches, the distance from the centre of the fulcrum to the valve is 3 inches, a 50 lb. weight is 30 inches from the fulcrum, what pressure will the valve hold?

3 diameter of valve.

3

9

.7854

36

45

72

63

7.0686 = area of valve.

3 ) 30

10

50 = weight

10 = leverage of weight.

Area of valve, 7.068 ) 500 .000 ( 70.7 = lbs. pressure per sq. in.

494 76

5 2400

4 9476

2924