Physics · Mechanical Properties Of Fluids · NEET
No, and mixing them up is the most common mistake. Speed of efflux v = sqrt(2gh) is how fast the jet comes out, measured in metres per second (m/s). Rate of flow Q is how much water (volume) leaves per second, measured in cubic metres per second (m3/s). You get Q by multiplying the speed by the hole area: Q = a x v = a x sqrt(2gh). So speed is a step on the way to the flow rate.
Always use the small HOLE area a, never the wide tank area. The water leaves through the hole, so the flow rate is the hole's cross-section times the jet speed. The tank's large top surface barely moves (its speed is almost zero because the tank is wide), so it does not go into this formula.
h is the vertical height of the water surface ABOVE the hole, not the full tank height (unless the hole is right at the bottom). If a tank is 2 m tall and full, and the hole is near the bottom, then h is about 2 m. If the hole were in the middle with 1.2 m of water above it, then h = 1.2 m. As the tank empties, h shrinks, so both v and Q slow down.
Torricelli's law comes from Bernoulli's equation, and it turns out the water leaves exactly as fast as an object that has fallen freely from height h. A freely falling body reaches v = sqrt(2gh) after falling h. The pressure of the water above the hole pushes the jet out at this same speed, which is why v = sqrt(2gh).
Convert everything to SI before multiplying. Area given as mm2 must become m2: 1 mm2 = 1 x 10^-6 m2, so 2 mm2 = 2 x 10^-6 m2. Height h in metres, g in m/s2. Then v comes out in m/s and Q = a x v comes out in m3/s. Doing the conversion first prevents answers that are off by a million.
A small hole of cross-sectional area 2 mm2 is present near the bottom of a fully filled open tank of height 2 m. Taking g = 10 m/s2, the rate of flow of water through the open hole would be nearly:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Cubic metres per second, written m3/s. It measures volume of liquid crossing the hole each second. Speed of efflux is different, measured in m/s.
No. As water drains out, the height h of water above the hole falls, so v = sqrt(2gh) drops and Q = a x sqrt(2gh) drops too. The jet gets slower and thinner over time.
Q = a x v, so doubling the hole area a doubles the rate of flow (h and v stay the same for a given water level). Twice the opening lets out twice the volume per second.
Then h is only the height of water above the hole, not the full tank height. A hole higher up has smaller h, so smaller v and a smaller flow rate Q.
For an open tank, no. Both v = sqrt(2gh) and Q = a x sqrt(2gh) contain no density term, so a light or heavy liquid leaves at the same speed and same volume rate for the same height h.
