Type a line (cooling load 12 kW delta T 10 K, duct 6 m/s) or fill in the fields: the line and the fields stay in step.
Enter a sensible load with a temperature difference, an air flow, a room size or a duct, and the calculator gives what is missing: the air flow for the load, the load or the temperature difference for an air flow, the air changes per hour of the room, the duct area, the round and rectangular duct sizes for a velocity, the velocity in an existing duct and the equivalent diameter of a rectangular one. Air flows in m3/h, m3/s, l/s and cfm, loads in kW, kcal/h and BTU/h. It shows the working with your numbers, draws the duct section to scale, and gives a line you can copy or add to a request.
The calculator gives no recommended air change rates or duct velocities: take them from the ship’s air handling design. The applicable standard sets the design conditions and the basis of calculation for the air conditioning and ventilation of accommodation spaces, and statutory rules can also apply to the ship. It works out sensible heat only, at the air density and specific heat it shows, without the latent heat of drying the air, and the clear inside section of a duct, with no pressure loss and no fan sizing.
The sensible load is Q = density x cp x V x delta T, in kW with V in m3/s. At 1.2 kg/m3 and 1.006 kJ/(kg K) the product is 1.2072 kJ/(m3 K). A cooling load of 12 kW at a difference of 10 K: V = 12 / (1.2072 x 10) = 0.9940 m3/s, or 3578 m3/h. The latent heat of moisture is not included.
The air changes per hour are the air flow in m3/h divided by the room volume: 1500 m3/h through a room of 4 x 3 x 2.5 m (30 m3) is 50 per hour. With the air changes entered it works the other way: air flow = air changes x volume. The calculator gives no recommended rates.
The area is A = V / v: 3600 m3/h at 8 m/s needs 0.125 m2, a round duct of 399 mm or a square one of 354 x 354 mm. A 400 x 300 mm duct at 2000 m3/h has 4.63 m/s, and its Huebscher equivalent diameter is De = 1.30 (a b)^0.625 / (a + b)^0.25 = 378 mm.
| Quantity | Relation | Note |
|---|---|---|
| Sensible load | Q = density x cp x V x delta T | kW with V in m3/s; 1.2 kg/m3 and 1.006 kJ/(kg K) unless entered |
| Air flow | V = Q / (density x cp x delta T) | m3/s; x 3600 for m3/h |
| Temperature difference | delta T = Q / (density x cp x V) | K; or the room minus the supply air |
| Air changes per hour | n = V / room volume | per hour, with V in m3/h and the volume in m3 |
| Duct area | A = V / v | m2, with V in m3/s and the velocity v in m/s |
| Round duct | d = square root of (4 A / pi) | a square duct has the side square root of A |
| Rectangular duct | b = A / a | for one side a entered; the velocity in an existing duct is V / A |
| Equivalent diameter | De = 1.30 (a b)^0.625 / (a + b)^0.25 | Huebscher: equal friction loss at equal air flow |
| Units | 1 cfm = 0.3048^3 / 60 m3/s = 1.699 m3/h; 1 l/s = 3.6 m3/h | 1 kcal/h = 1.163 W; 1 BTU/h = 0.2930711 W |
The density 1.2 kg/m3 (standard air at 20 °C and 1013 mbar) and the specific heat 1.006 kJ/(kg K) are used unless others are entered. Duct sizes are the clear inside section. 1 ft = 0.3048 m exactly; the kcal is the international one, 4.1868 kJ.
The sensible heat Q = m cp delta T and the split into sensible and latent heat come from general heat transfer and air conditioning references, which give the specific heat of air as 1.006 kJ/(kg K) and its density as about 1.2 kg/m3. The same specific heat, 1006 J/(kg K), and the density 1.2 kg/m3 are used in an open building simulation library, and 1.2 kg/m3 at 20 °C and 1013 mbar is the standard air density in a guide to local exhaust ventilation. The air changes per hour as the air flow divided by the volume, and the relation of flow, velocity and area, Q = v A, are given in engineering references and in encyclopaedia articles. The equivalent diameter is the Huebscher relation (1948), given alike in two independent engineering references and checked with 300 x 500 mm = 420 mm. The unit factors follow national tables of conversion to SI units (1 ft = 0.3048 m, the international calorie = 4.1868 J, 1 BTU/h = 0.2930711 W). That the applicable standard sets the design conditions and the basis of calculation for ship accommodation air conditioning and ventilation, and that statutory rules can apply to the ship, comes from the scope of the standard as two national standards catalogues list it; the scope names no air change rates or velocities.
From the sensible heat of the air: Q = m cp delta T with the mass flow m = density x V, so Q in kW = density x cp x V x delta T with V in m3/s. For the air flow, V = Q / (density x cp x delta T). A cooling load of 12 kW with a temperature difference of 10 K between the room and the supply air: V = 12 / (1.2 x 1.006 x 10) = 0.9940 m3/s, or 3578 m3/h. The same relation gives the load for an air flow and a temperature difference, or the difference for a load and an air flow. It is sensible heat only: the latent heat of the moisture taken out of the air is not included.
Unless other values are entered, 1.2 kg/m3, the standard air density at 20 °C and 1013 mbar, and 1.006 kJ/(kg K) for the specific heat of air; together 1.2 x 1.006 = 1.2072 kJ/(m3 K), so 1 m3/s of air warmed or cooled by 1 K takes up or gives off about 1.21 kW. When the design works with other values, enter them in the line (density 1.16 kg/m3 cp 1.005) or in the fields, and the working uses them.
The air changes per hour are the air flow in m3/h divided by the room volume in m3: 1500 m3/h through a room of 4 x 3 x 2.5 m, 30 m3, is 50 air changes per hour. With the air changes entered, the calculator gives the air flow instead: 10 per hour in 30 m3 is 300 m3/h. It gives no recommended rates: take them from the ship’s air handling design; the applicable standard sets the design conditions and the basis of calculation for the air conditioning and ventilation of accommodation spaces.
The duct area is the air flow divided by the velocity, A = V / v. The round duct diameter is then the square root of 4 A / pi, and a square duct has the side the square root of A; with one side of a rectangular duct entered, the other side is A divided by it. For 3600 m3/h at 8 m/s: V = 1 m3/s, A = 0.125 m2, a round duct of 399 mm or a square duct of 354 x 354 mm. In an existing duct the calculator gives the velocity, V / A. It gives no recommended velocities: take them from the design of the system.
The round duct with the same friction loss per metre at the same air flow, by the Huebscher relation De = 1.30 (a b)^0.625 / (a + b)^0.25, in any one unit. For a 400 x 300 mm duct, De = 378 mm. It is not the duct of the same area: the round duct of 378 mm has 0.1120 m2 against 0.12 m2, so at 2000 m3/h the air runs at 4.96 m/s in it and at 4.63 m/s in the rectangular duct.
Air flows in m3/h, m3/min, m3/s, l/s and cfm (1 cfm = 1.699 m3/h); loads in kW, W, kcal/h (1 kcal/h = 1.163 W) and BTU/h (1 BTU/h = 0.2931 W); the temperature difference in K, or the supply and room temperatures in °C, °F or K; the room as length x width x height in m, or its volume in m3, with the air changes per hour; duct sizes in mm, cm or m, a round diameter, a x b or one side; the velocity in m/s or ft/min; and, if wanted, the air density in kg/m3 and the specific heat in kJ/(kg K).
The calculator gives the air flow, the load and the duct section. When parts for a fan, an air cooler, dampers or ducting are needed, send the line from the calculator with the unit details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
