A 6indiameter piston is located within a cylinder which is c

A 6-in.-diameter piston is located within a cylinder which is connected to a 1/2-in.-diameter inclined-tube manometer as shown in the figure below. The fluid in the cylinder and the manometer is oil (specific weight = 59 lb/ft^3) When a weight, W, is placed on the top of the cylinder, the fluid level in the manometer tube rises from point (1) to (2). How heavy is the weight? Assume that the change in position of the piston Is negligible.

Solution

specific weight (also weight per unit volume) is 59 lb/ft^3.

The weight acted on the piston is equal to the weight of the liquid displaced.

Let us find the volume of the liquid displaced = 6\" * (1/2)\" =3 inch^3 (Even the tube is inclidened the volume change is straight forward).

Now convert the units of the given specific gravity into inches = 0.034144 lb/in^3

Volume = 3 inch cube

So, weight W = 0.034144*3 = 0.1024 lbs