Wave Power Formula

Wave power is a form of renewable energy which are produced from the motion of ocean waves, created by the wind blowing across the sea’s surface. This energy can be harnessed to generate electricity, pump water, or even desalinate seawater. Measured in watts (W), wave power is basically the energy transferred through the ocean’s waves. Unlike tidal energy, which is driven by the gravitational pull of the moon, wave power is generated by the wind’s interaction with the water. This energy is captured by specialised machines called wave energy converters, which makes wave power a viable and sustainable clean energy option for the future.

Formula,

where,

P is the wave power,

T is the period of wave,

H is the height of wave,

L is the wavefront length,

ρ is a constant, that is, water density with a value of 1.025 kg/m³,

g is the acceleration due to gravity with a value of 9.8 m/s²,

π is a constant with the value of 3.14.

Wave Power Dimensional Formula ,

The dimension of density is mass per unit volume:

[ρ]=[ML⁻³]

The dimension of acceleration is length divided by time squared:

[g]= [LT⁻²]

This is a length, so its dimension is:

[H]=[L]

The dimension of speed is length divided by time:

[c]=[LT⁻¹]

Now, we substitute these dimensional expressions into the wave power formula:

[P]=1/2 ​[ρ][g][H]²[c]

[P]=1​/2 (ML−³⁾(LT⁻²⁾(L²⁾(LT⁻¹)

Simplifying this:

[P]=[ML²T⁻³]

Sample Problems

Problem 1. Find the wave power of a wave of length 8 m at a height of 10 m in 3 seconds.

Solution:

We have,

l = 8

h = 10

T = 3

Using the formula we have,

P = ρg²Th²l / 32π

= (1.025 × 9.8 × 9.8 × 3 × 10 × 10 × 8) / (32 × 3.14)

= 236258.4/100.48

= 2351.29 W

Problem 2. Find the wave power of a wave of length 5 m at a height of 7 m in 4.5 seconds.

Solution:

We have,

l = 5

h = 7

T = 4.5

Using the formula we have,

P = ρg²Th²l / 32π

= (1.025 × 9.8 × 9.8 × 4.5 × 7 × 7 × 5) / (32 × 3.14)

= 108531.20/100.48

= 1080.127 W

Problem 3. Find the length of a wave of power 2000 W at a height of 3 m in 10 seconds.

Solution:

We have,

P = 2000

h = 3

T = 10

Using the formula we have,

P = ρg²Th²l / 32π

=> 2000 = (1.025 × 9.8 × 9.8 × 10 × 3 × 3 × l) / (32 × 3.14)

=> 8859.69 l/100.48 = 2000

=> 88.17 l = 2000

=> l = 22.6 m

Problem 4. Find the length of a wave of power 3450 W at a height of 4 m in 12 seconds.

Solution:

We have,

P = 3450

h = 4

T = 12

Using the formula we have,

P = ρg²Th²l / 32π

=> 3450 = (1.025 × 9.8 × 9.8 × 12 × 4 × 4 × l) / (32 × 3.14)

=> 18900.67 l/100.48 = 3450

=> 188.10 l = 3450

=> l = 18.34 m

Problem 5. Find the height of a wave of power 4561 W if its length is 9 m in 4 seconds.

Solution:

We have,

P = 4561

l = 9

T = 4

Using the formula we have,

P = ρg²Th²l / 32π

=> 4561 = (1.025 × 9.8 × 9.8 × 4 × h² × 9) / (32 × 3.14)

=> 3543.876 h²/100.48 = 4561

=> 35.26 h² = 4561

=> h² = 129.35

=> h = 11.37 m

Problem 6. Find the height of a wave of power 7631 W if its length is 2 m in 7 seconds.

Solution:

We have,

P = 7631

l = 2

T = 7

Using the formula we have,

P = ρg²Th²l / 32π

=> 7631 = (1.025 × 9.8 × 9.8 × 2 × h² × 7) / (32 × 3.14)

=> 1378.174 h²/100.48 = 7631

=> 13.71 h² = 7631

=> h² = 556.60

=> h = 23.59 m

Problem 7. Find the time taken by the wave of length 4.5 m to generate power of 3265 W at a height 14 m.

Solution:

We have,

P = 3265

l = 4.5

h = 14

Using the formula we have,

P = ρg²Th²l / 32π

=> 3265 = (1.025 × 9.8 × 9.8 × T × 14 × 14 × 4.5) / (32 × 3.14)

=> 86824.962 T/100.48 = 3265

=> 864.101 T = 3265

=> T = 3.77 s