The water is supplied at a pressure of 15 N/cm² to an accumulator, having a ram of diameter 2.0 m. If the total lift of the ram is 10 m, determine : (a) the capacity of the accumulator, and (b) total weight placed on the ram

Hydraulic Accumulator Calculation

Problem Statement

The water is supplied at a pressure of 15 N/cm² to an accumulator, having a ram of diameter 2.0 m. If the total lift of the ram is 10 m, determine : (a) the capacity of the accumulator, and (b) total weight placed on the ram (including the weight of the ram).

Given Data & Constants

Water pressure, $P = 15 \, \text{N/cm}^2$
Diameter of ram, $D = 2.0 \, \text{m}$
Lift of ram, $L = 10 \, \text{m}$

Solution

1. Convert Pressure to Standard Units (N/m²)

$$ P = 15 \, \frac{\text{N}}{\text{cm}^2} \times \frac{10000 \, \text{cm}^2}{1 \, \text{m}^2} = 150000 \, \text{N/m}^2 $$

2. Calculate the Area of the Ram (A)

$$ A = \frac{\pi}{4} D^2 = \frac{\pi}{4} (2.0)^2 \approx 3.1416 \, \text{m}^2 $$

(b) Total Weight Placed on the Ram (W)

The total weight on the ram is the force required to create the specified pressure over the area of the ram.

$$ W = P \times A $$ $$ W = 150000 \, \text{N/m}^2 \times 3.1416 \, \text{m}^2 $$ $$ W = 471240 \, \text{N} $$

(a) The Capacity of the Accumulator

The capacity of the accumulator is the total energy it can store, which is the work done in lifting the weight.

$$ \text{Capacity (Energy)} = \text{Weight} \times \text{Lift} = W \times L $$ $$ \text{Capacity} = 471240 \, \text{N} \times 10 \, \text{m} = 4712400 \, \text{Nm} $$ $$ \text{Capacity} = 4712.4 \, \text{kNm} $$

Final Results:

(a) Capacity of the accumulator: $ \approx 4712.4 \, \text{kNm} $

(b) Total weight on the ram: $ 471240 \, \text{N} $ (or $471.24 \, \text{kN}$)

Explanation of a Hydraulic Accumulator

A hydraulic accumulator is essentially a hydraulic energy storage device. It works like a temporary battery for a hydraulic system. A pump supplies fluid to the accumulator, and the pressure of this fluid lifts a very heavy weight (the ram and additional weights). This process stores potential energy in the lifted weight.

When a machine (like a hydraulic press or crane) needs a large amount of fluid at high pressure for a short period, the accumulator releases its stored energy. The heavy weight pushes down on the ram, forcing the fluid out at high pressure. This allows the system to deliver a high power output without needing an enormous pump that would be idle most of the time.

Capacity: This refers to the energy storage of the device (Work = Force x Distance).
Weight: The massive weight on the ram is what maintains the constant high pressure in the system.